@@SquidInkSpaghettithat’s because with the parenthesis they can be simplified to a positive number with that exponent. If you didn’t have any parenthesis you would still get a negative, which you can’t have in a radical, so you can still pull out an i (imaginary number) and then just square root the 25 which is 5 since (5and5) can go into a group. And then just remember to put the imaginary number after the 5. That’s the way I was taught at least, so similarly to how you were taught. 😂
@@flarklooneyyeah you can’t have negatives in a radical, so you can always just say -1 (which represents your i) times whatever number is being square rooted. And then once your done square rooting and simplifying, you can put in your imaginary number, it just can’t be the first thing your equation.
@@lj1687I would say yes because -(3)^2 will equal -9 still or in other words -1 (3X3) and then according to PEMDAS, you simplify your parenthesis, then multiply your -1 to what is in the parenthesis. So you would still get the right answer. I hope that helps!
If there is possibility of misinterpretation, disambiguating parentheses must be used. This is the PRIMARY guiding principle of mathematics formulas. It takes precedence over all other rules. There are programs and conventions that do or have interpreted this in different ways. Therefore, there is a possibility of misinterpretation. Run this through the unix bc (binary calculator), and you will get 5. Run this through mathematica, and you will get 5i. Look at early mathematics papers and you can find different interpretations of the core concept. Look at older arithmetic books and you will find different interpretations of the core concept. Order of operations for negative integers in arithmetic prior to algebra is not properly defined (as compared to algebra, where the variables make one interpretation more common) The question posed is therefore badly formed.
@@AuroraNora3 yes, and the only way I know of that even has the potential of disambiguating the two scenarios is splitting the meanings of those two phrases so that are currently equivalent.
@@kujmousThere is but it is sometimes confusing. There are some scenarios where parentheses are pronounced as "quantity". Example 3(2x+1) This is pronounced as 3 times the quantity of 2x plus 1
This is true, but the closing of parentheses or radicals becomes a matter of inflection. It may just be a matter of understanding that we have to lose some precision when speaking. For instance, how would we speak "7((x+y)-(a+b))"?
no, wrong. The minus is not an operator, it is a component of the number to square. So it is (d), because the origin equation does not play any role. Two failure in one equation. respect.
@@dizzi5842you are wrong. -5² =-(5)² =-25 You shouldn't square the "-" unless the question is (-5)² In which case, the answer would be... (-5)² =(-5)(-5) =+25 So the answer to the question is 5. Explanation: √-5² = i√5² ,where i=√-1 =5i
@@ShanthiVeluswamy -5² is not -1*5² because you can write it as x² with x=-5. Here the minus is an algebraic sign not a substraction. Just because math programs and calculators need help by parenthesis, doesn't mean implicitness notations are worthless.
@@dizzi5842 if you want to write x² where x is 5, then it should be written as X²=(-5)² =+25 But if there is no brackets, -5²=-5*5 =-25 If you still don't believe me, use a calculator or Google and check it for yourself.
Since the -3 isn’t in parentheses you can treat his example of -3^2 as -1 * 3^2 making it -9. This is also due to the fact that by default, the exponent comes before the negative symbol or as per the scenario mentioned, the exponent comes before the multiplication like in the order of operations. To make it into the square of -3, the -3 would need to be put in the parentheses which in that case would make it positive 9.
Not a confusing issue per se, it's a question about notation and interpretation. And I still don't like it. This way negative numbers don't exists anymore, or can't be represented anymore, but there are only positive numbers multiplied by -1. The confusing thing is why we should accept that.
@@RonaldABG Why not? It is not that Maths is afraid of new, strange symbols. As an example, you can use the single dash/hyphen "-" for as a negative sign, and the wide one "-" or the even longer one "-" I don't know its name or use in English, I will call it superminus (just because I like it) as subtraction sign, the minus. It's obviously those are too similar to be effective, when handwritten would be a mess, so just pretend it is the choice for the sake of the example. So we would have a 5 - 2 = 3 and a 5 - -2 = 7, at which point the operator must be expressed because 5 - -2 = -10, (2 - 3²) = -7, (2 + -3²) = 11. If you want to isolate the negative sign, you'll have to use parentheses, -3² = 9, -(3²) = -9 I feel so much more correct to me because the negative sign is an intrinsic characteristic of the number not an operator while the minus sign is another operator and you have to force the representation of the sign if you want to be processed outside the square root. Now it can follow the padmas or what the heck in english you name the sequence.
1) We do the action inside the square root : Sqrt (-5^2) = Sqrt [-(5^2)] = Sqrt (-25) 2) Since - 25 is a negative number we won't have a real solution so we will use the imaginery number (i): Sqrt (-25) = Sqrt 25 × Sqrt (-1) = 5i Answer: B) 5i
-'ve sign under square root, will give an "i"... And we have only one choice in the answer options, which has an "i".. Option (b) 5i , is correct answer
Yikes! First time in 37 years I got a math problem right. That is if the answer is 5i. Just as a boring note, Godzilla 5i is now playing at a theater near you.
Guys and gals, I finished high school before the millennium but I do remember that a negative integer squared equals to a positive integer. Given that... √-5²=√25=+/-5 right? The square power is inside the root, not above it to handle it with i.
Just wondering, you know how root 16 is only +4, but sometimes the solutions to an answer are +5 or -5 (for example), when is it only the positive solution and when is it both positive and negative solution?
a) treat - as a minus sign. You don’t say that 0-5^2 is 0+(-5)^2. -5^2 is -25, not 25. Therefore, it is not sqrt((-5)^2)=sqrt(25)=5 b) is correct. sqrt(-5^2) = sqrt(-25) = sqrt(-1) * sqrt(25) = 5i (i is the imaginary unit) c) sqrt(-x) is not -sqrt(x), it is i sqrt(x). Don’t make that mistake. d) is wrong because i) it is not sqrt(25) in the first place, and ii) the square root function only gives the primary solution (i.e. it is not multivalued)
But, if we are in the set of complex numbers, the resulting square root would be bi-valued, that is, it would have 2 possible values: ±5i, right? I say because the answer here is the alternative: b) 5i, which is an imaginary number, and at the same time it is a complex number.
It's b, but when we take the nth root of a+bi, there's not much documentation on what it actually is. There's n different nth roots of a+bi (if it's nonzero) so I take the one with the smallest positive argument. This ties in nicely with the square root of positive real numbers, eg 25 has two square roots, but the actual Sqrt of 25 is 5, as that has an argument of 0 when viewed as a complex number, whereas -5 has an argument of pi, so 5 has the smallest positive argument.
Im confuse... If we use the rule ³√a²=a^⅔ Then √-5²=-5^2/2=-5 But the answer is can be 5i too Im confusing with the rule -5²=-25 and (-5)²=25 We all know that √-25 is 5i but following what i have write before; -5²=-25, that mean √-25=-5 Can someone explain
You know that rule where you can’t break a positive number inside the square root radical and then distribute the square root radical? Well, I can use that to prove that, say, sqrt(36)=+6 So sqrt(36) ≠ sqrt(-6)*sqrt(-6) sqrt(36) ≠ sqrt(6)*sqrt(6)*i*i +-6 ≠ -6 But -6=-6 so, 6 ≠ -6 So, logic suggests sqrt(36) ≠ -6
By definition, square roots of 36 are ±6. But when we use the radical sign, √, we only use the positive root or the principal root. Meaning √36 is only equal to +6. ± is added only when solving an equation.
A negative number squared is always positive. I hate how math is using ambiguous notation which requires insider knowledge to understand. Here are edits which I think need to be made: -n^2 = (n x n) -(n)^2 = -1 (n x n) a / bc = a / (bc) (a/b)c = ac / b
A minus ain't squared, unless it's been snared. Nothing ambiguous about that, it's a standard convention to follow. It's no more ambiguous and insider knowledge, than knowing that you need to drive on the right in the USA, and drive on the left in the UK. Math has rules of the road, just like actual roads have rules of the road.
@@NicholasOfAutrecourt A minus ain't squared, unless it's been snared. -5^2 doesn't mean a negative 5 is squared. It means you first square the 5, and then negate it.
@@ShanthiVeluswamy sorry but you can’t. I’m a french mathematician sudent and you can’t do that. i isn’t defined as sqrt(-1) but i is defined as i^2 = -1. We are doing that because it’s absolutely illégal to put negatine numbers under square root. If you do it, you can show that 1 = -1. That’s why it’s prohibited. Let me show you: sqrt(-1) * sqrt(-1) = (sqrt(-1))^2 = -1 But, you have also: sqrt(-1) * sqrt(-1) = sqrt(-1 * -1) = sqrt(1) = 1 So 1 = -1. There is absolutely no error of calcul. Here is what append when you put negative Numbers under sqrt. Another way to show it is the following: Everyone know that sqrt is power 1/2 But when the power is not an integer, it’s defined like that: x^n = exp(n * ln(x)) and what’s ln(x) if x is negative ? This is undefined. Like x^(1/2) is not defined if x is negative. So, i’m not an amateur, i’m doing high level mathematics everydays with highly qualified teachers. So when i tell you that you can’t do that, actually, you really can’t.
@@varfarrog4544 √-1*√-1 does not equal √(-1*-1) You can only combine the root(√) when atleast one of the 2 numbers in positive. In this case, both of the numbers are negative. i.e. √a*√b=√ab only holds true when atleast 1 of them is positive. You said that i²=-1 That implies i=√-1 You can use other websites to verify this and for the problem mentioned in the video, the answer is 5i Also I didn't think that you are immature or weak at math.
@@ugonnahart3908 -3^2 and (-3)^2 are different because the one without paranthesis is only applying to the 3, not the negative, while the one with paranthesis is applying to the negative AND 3 -3^2=-1(3^2)=(-1)(9) (-3)^2=(-1)^2 (3)^2=(1)(9)
A minus ain't squared, unless it's been snared. In this case, the -5 isn't squared together, when written as -5^2. Only the 5 is squared. The minus is applied after the squaring. Since it is so much more common that you prefer signs to be applied after exponents, it is convention that you have to snare your negative signs, if you want them raised to any power. Thus, you'd have to write it as sqrt((-5)^2), if you wanted two negatives to multiply to be a positive in an example similar to the given one.
@@mrhtutoring: I’m a bit confused as well . There was an example of : If x = -3 , then what is x^2 . And your answer was 9, not -9 . And now you have this -3^2 is -9 .
i is the square root of -1, also known as the imaginary unit. This isn't a real number, so we can't reduce it any further than i. Don't let the name deceive you, just because we call it imaginary. That was just a name coined by a critic, that somehow stood the test of time, when people first came up with the idea of imaginary numbers. There are plenty of practical applications of these numbers
![Why you didn't learn tetration in school[Tetration]](http://i.ytimg.com/vi/Ea1_1aVfwl4/mqdefault.jpg)
The correct answer is (b) 5i.
Yes I get it right ✅️ 🎊👌
now all that is left is to attend the Korean CSAT😅
Ahh ye, i thought it was “-(5^2)”, ohh. It’s not the same as -5^2
5i
Why not ±5i
@@prithvisinghpanwar6609 why would it
√-5²=√-1x5²
√-1x5²=√-1√5²
√-1√5²=i(5)
i(5)=5i
Your explanation is *_exactly_* what we needed. Thank You!
i was taught to just treat it like its -(5)^2 and that the exponent does not affect the 5 so i just did sqrt(-25)
@@SquidInkSpaghettithat’s because with the parenthesis they can be simplified to a positive number with that exponent. If you didn’t have any parenthesis you would still get a negative, which you can’t have in a radical, so you can still pull out an i (imaginary number) and then just square root the 25 which is 5 since (5and5) can go into a group. And then just remember to put the imaginary number after the 5. That’s the way I was taught at least, so similarly to how you were taught. 😂
@@flarklooneyyeah you can’t have negatives in a radical, so you can always just say -1 (which represents your i) times whatever number is being square rooted. And then once your done square rooting and simplifying, you can put in your imaginary number, it just can’t be the first thing your equation.
-1^2x5^2 isnt it have to be like that
If you don't understand -3^2=-9
It's -1×3^2=-9 and because power comes before multiplication it becomes a negative number
Think of it as -x^2 is 0-x^2. Treat the - sign as a minus and you’re good for any tricks like this
Then shouldn't the 3 be in a parentheses. 🫤
@@lj1687I would say yes because -(3)^2 will equal -9 still or in other words -1 (3X3) and then according to PEMDAS, you simplify your parenthesis, then multiply your -1 to what is in the parenthesis. So you would still get the right answer. I hope that helps!
@@kalebcarpenter3920 oh now I remembered -(3)^2 = -9 and (-3)^2 = 9.
@@kalebcarpenter3920 the lack of parentheses was throwing me off. Ty
If there is possibility of misinterpretation, disambiguating parentheses must be used. This is the PRIMARY guiding principle of mathematics formulas. It takes precedence over all other rules.
There are programs and conventions that do or have interpreted this in different ways. Therefore, there is a possibility of misinterpretation.
Run this through the unix bc (binary calculator), and you will get 5. Run this through mathematica, and you will get 5i. Look at early mathematics papers and you can find different interpretations of the core concept. Look at older arithmetic books and you will find different interpretations of the core concept.
Order of operations for negative integers in arithmetic prior to algebra is not properly defined (as compared to algebra, where the variables make one interpretation more common)
The question posed is therefore badly formed.
if only there were a way to verbalize parentheses...
I have to fight the urge to think of "negative three" as the base. I would've said "the opposite of three squared is negative nine."
@@kujmous could still be interpreted as (the opposite of three)²
@@AuroraNora3 yes, and the only way I know of that even has the potential of disambiguating the two scenarios is splitting the meanings of those two phrases so that are currently equivalent.
@@kujmousThere is but it is sometimes confusing. There are some scenarios where parentheses are pronounced as "quantity". Example
3(2x+1)
This is pronounced as 3 times the quantity of 2x plus 1
This is true, but the closing of parentheses or radicals becomes a matter of inflection. It may just be a matter of understanding that we have to lose some precision when speaking. For instance, how would we speak "7((x+y)-(a+b))"?
You have very very interesting points about very basics in maths.
It's because I teach these basic math day in and day out.
Option: b. 5i 🎉🎉❤❤
First answer 😂
too easy
no, wrong. The minus is not an operator, it is a component of the number to square. So it is (d), because the origin equation does not play any role. Two failure in one equation. respect.
@@dizzi5842you are wrong.
-5² =-(5)²
=-25
You shouldn't square the "-" unless the question is (-5)²
In which case, the answer would be...
(-5)² =(-5)(-5)
=+25
So the answer to the question is 5.
Explanation:
√-5² = i√5² ,where i=√-1
=5i
@@ShanthiVeluswamy -5² is not -1*5² because you can write it as x² with x=-5. Here the minus is an algebraic sign not a substraction. Just because math programs and calculators need help by parenthesis, doesn't mean implicitness notations are worthless.
@@dizzi5842 if you want to write x² where x is 5, then it should be written as
X²=(-5)²
=+25
But if there is no brackets,
-5²=-5*5
=-25
If you still don't believe me, use a calculator or Google and check it for yourself.
The right answer is 5i, since √- 5² = √- 25 = 5. √- 1 = 5i
Since the -3 isn’t in parentheses you can treat his example of -3^2 as -1 * 3^2 making it -9. This is also due to the fact that by default, the exponent comes before the negative symbol or as per the scenario mentioned, the exponent comes before the multiplication like in the order of operations. To make it into the square of -3, the -3 would need to be put in the parentheses which in that case would make it positive 9.
👍💯
5i but i loved how you gave us all the necessary bits in advance 😁
Not a confusing issue per se, it's a question about notation and interpretation. And I still don't like it.
This way negative numbers don't exists anymore, or can't be represented anymore, but there are only positive numbers multiplied by -1.
The confusing thing is why we should accept that.
Would you like to have an additional symbol to distinguish between the minus operation and the - of the negative numbers?
@@RonaldABG Why not? It is not that Maths is afraid of new, strange symbols.
As an example, you can use the single dash/hyphen "-" for as a negative sign, and the wide one "-" or the even longer one "-" I don't know its name or use in English, I will call it superminus (just because I like it) as subtraction sign, the minus. It's obviously those are too similar to be effective, when handwritten would be a mess, so just pretend it is the choice for the sake of the example.
So we would have a 5 - 2 = 3 and a 5 - -2 = 7, at which point the operator must be expressed because 5 - -2 = -10, (2 - 3²) = -7, (2 + -3²) = 11. If you want to isolate the negative sign, you'll have to use parentheses, -3² = 9, -(3²) = -9 I feel so much more correct to me because the negative sign is an intrinsic characteristic of the number not an operator while the minus sign is another operator and you have to force the representation of the sign if you want to be processed outside the square root.
Now it can follow the padmas or what the heck in english you name the sequence.
I failed the exam after seeing this video 💀
I thought the same broh
1) We do the action inside the square root :
Sqrt (-5^2) = Sqrt [-(5^2)] = Sqrt (-25)
2) Since - 25 is a negative number we won't have a real solution so we will use the imaginery number (i):
Sqrt (-25) = Sqrt 25 × Sqrt (-1) = 5i
Answer: B) 5i
The negative sign isn't inside the bracket. That's why it will be root of -25. So the answer is 5i so B.
-'ve sign under square root, will give an "i"... And we have only one choice in the answer options, which has an "i"..
Option (b) 5i , is correct answer
Yikes! First time in 37 years I got a math problem right. That is if the answer is 5i. Just as a boring note,
Godzilla 5i is now playing at a theater near you.
C. -5 I think is the answer!
Guys and gals, I finished high school before the millennium but I do remember that a negative integer squared equals to a positive integer.
Given that... √-5²=√25=+/-5 right?
The square power is inside the root, not above it to handle it with i.
The answer is B because u actually do 5 squared which gets 25 and the negative turns it into -25 and the square root of that is 5i
5i.
Breakdown -
sqrt(-5^2) {original equation}
sqrt(-1)sqrt(5^2) {-5^2 is actually -1 multiplied by 5^2}
sqrt(-1) is i
sqrt(5^2) is 5
i(5) = 5i
Why do people write sqrt when there is a square root symbol √ and an indices converter ², are you on a laptop?
@@pigeonlove desktop and the ASCII did not help.
B
5i
Option 'B'
Once again it is down to definitions of notation. People remember or learned it differently. This is not a math question.
❤❤😢A
I agree with you Sensei.
Just wondering, you know how root 16 is only +4, but sometimes the solutions to an answer are +5 or -5 (for example), when is it only the positive solution and when is it both positive and negative solution?
When you want to x2 you have + / -
@@michelmulder5770 wdym x2?
√16 is 4. But if x^2 is 16 then x is+4 and -4.
@@harrymatabal8448 What is the reason -4 can't be the root of 16?
@@harrymatabal8448 o thankss, but is there a reason why? Whats the difference between them
What you're telling me is that I've been doing this wrong during my whole school life..? Now I'm questioning my whole existence.
a) treat - as a minus sign. You don’t say that 0-5^2 is 0+(-5)^2. -5^2 is -25, not 25. Therefore, it is not sqrt((-5)^2)=sqrt(25)=5
b) is correct. sqrt(-5^2) = sqrt(-25) = sqrt(-1) * sqrt(25) = 5i (i is the imaginary unit)
c) sqrt(-x) is not -sqrt(x), it is i sqrt(x). Don’t make that mistake.
d) is wrong because i) it is not sqrt(25) in the first place, and ii) the square root function only gives the primary solution (i.e. it is not multivalued)
Answer is 5i.
Usually, the Square Root of a number will always return an error.
The answer is (b) is 5i
But, if we are in the set of complex numbers, the resulting square root would be bi-valued, that is, it would have 2 possible values: ±5i, right? I say because the answer here is the alternative: b) 5i, which is an imaginary number, and at the same time it is a complex number.
b.5i
Solution:
√-5²=√-25=√-1 . √25 = i . 5 = 5i
-5 is the current answer
No, the answer is 5i,
Where i=√-1
It's b, but when we take the nth root of a+bi, there's not much documentation on what it actually is.
There's n different nth roots of a+bi (if it's nonzero) so I take the one with the smallest positive argument.
This ties in nicely with the square root of positive real numbers, eg 25 has two square roots, but the actual Sqrt of 25 is 5, as that has an argument of 0 when viewed as a complex number, whereas -5 has an argument of pi, so 5 has the smallest positive argument.
b
Option (b)
Which is the right interpretation a:(-5)^2 or b: -(5)^2-where it’s only one negative not squared?
If there is no bracket, then only the number is squared not the negative sign.
@@catherinemarsh5453 thanks for confirming
B 5i
D
imo when you write -3 it is a negative number because that's what the sign means. If I write 5-3, that simply means 5 + (-3).
Im confuse...
If we use the rule ³√a²=a^⅔
Then √-5²=-5^2/2=-5
But the answer is can be 5i too
Im confusing with the rule -5²=-25 and (-5)²=25
We all know that √-25 is 5i but following what i have write before; -5²=-25, that mean √-25=-5
Can someone explain
Following the order of operation, -5² inside the square root must be completed first.
x^2=-5^2 would be +/- 5i though. So in this definition sqrt() isn't the inverse operation of ^2.
should be 5i from what I understand.
Don’t believe in computer algebra systems, believe in math!
Option (b) 5i
5
You know that rule where you can’t break a positive number inside the square root radical and then distribute the square root radical?
Well, I can use that to prove that, say, sqrt(36)=+6
So sqrt(36) ≠ sqrt(-6)*sqrt(-6)
sqrt(36) ≠ sqrt(6)*sqrt(6)*i*i
+-6 ≠ -6
But -6=-6 so,
6 ≠ -6
So, logic suggests sqrt(36) ≠ -6
-5 squared is -25
Square root (you can look at the examples he put underneath) of -25 is 5i
B
A
Got it
±5i
5 because of the property √x²=|x| so here we take x to be -5 ,then modulus of -5 is 5🤓
How!!!!!!!!!!!! 😮😮😮😮
B) i5
b) 5i
Sir help me
If A is 1/(1/2024+1/2023…..+1/2001+1/2000),
Then if the integer A is divided by 48 what’s the remainer?
A isn't an integer
B 5i ..but not so sure
Only (b)
Why is the Square Root of 36 only positive 6? When we use the quadratic formula, it's always plus or minus. 🤔
By definition, square roots of 36 are ±6. But when we use the radical sign, √, we only use the positive root or the principal root. Meaning √36 is only equal to +6.
± is added only when solving an equation.
B!!!!!!
b because -5^2=-25, sqrt(-25)=5i
(B) 5i
i dont disagree i just wanna know whyyyyy? im curious
5i for surr
b) √-5² = √-25 = √-1. √25 = 5i
C option
+5
This is right answer 5iora (5i) this is right option b is😊😊
5i?
5!
(b)
The correct answer is b=5i, because 5i^2^1/2 is 5i
b is the answer
A negative number squared is always positive. I hate how math is using ambiguous notation which requires insider knowledge to understand. Here are edits which I think need to be made:
-n^2 = (n x n)
-(n)^2 = -1 (n x n)
a / bc = a / (bc)
(a/b)c = ac / b
A minus ain't squared, unless it's been snared. Nothing ambiguous about that, it's a standard convention to follow.
It's no more ambiguous and insider knowledge, than knowing that you need to drive on the right in the USA, and drive on the left in the UK. Math has rules of the road, just like actual roads have rules of the road.
Negative inside square root is not a real number, so likely answer b is the only correct option
Except that √((-5)^2) is 5, not 5i.
@@NicholasOfAutrecourt you are placing parenthesis in the equation as if you're allowed to... you realize that affects how its calculated?
@@NicholasOfAutrecourt A minus ain't squared, unless it's been snared.
-5^2 doesn't mean a negative 5 is squared. It means you first square the 5, and then negate it.
@@carultch I'm well aware. I used to teach high school students this stuff. But thanks.
What if the square is outside the root
Then it would simplify to -5.
@@mrhtutoring oh ok
When in doubt, use parentheses. Don't make me guess what the problem is asking.
If you know the rules, no need for extra parentheses.
@@mrhtutoring I know the rules; this is an Algebra problem, not Arithmetic.
why isn't ±5i correct?
If you had the equation x²=-25, x would equal ±5i.
But when simplifying √-25 without the equation, it's only equal to 5i.
the sqrt() function can only spit out positive numbers
You just can’t put a negative number under a square root it’s the rule si there is no good or bad answer it’s just undefined.
You can, mathematicians have defined the square root of negative numbers.
√-1= i
So the answer is..
√-5² =√-25
=√-1*√25
=5i
@@ShanthiVeluswamy sorry but you can’t. I’m a french mathematician sudent and you can’t do that. i isn’t defined as sqrt(-1) but i is defined as i^2 = -1. We are doing that because it’s absolutely illégal to put negatine numbers under square root. If you do it, you can show that 1 = -1. That’s why it’s prohibited. Let me show you:
sqrt(-1) * sqrt(-1) = (sqrt(-1))^2 = -1
But, you have also:
sqrt(-1) * sqrt(-1) = sqrt(-1 * -1) = sqrt(1) = 1
So 1 = -1. There is absolutely no error of calcul. Here is what append when you put negative Numbers under sqrt.
Another way to show it is the following:
Everyone know that sqrt is power 1/2
But when the power is not an integer, it’s defined like that:
x^n = exp(n * ln(x)) and what’s ln(x) if x is negative ? This is undefined. Like x^(1/2) is not defined if x is negative.
So, i’m not an amateur, i’m doing high level mathematics everydays with highly qualified teachers. So when i tell you that you can’t do that, actually, you really can’t.
@@varfarrog4544
√-1*√-1 does not equal
√(-1*-1)
You can only combine the root(√) when atleast one of the 2 numbers in positive. In this case, both of the numbers are negative. i.e.
√a*√b=√ab only holds true when atleast 1 of them is positive.
You said that i²=-1
That implies i=√-1
You can use other websites to verify this and for the problem mentioned in the video, the answer is 5i
Also I didn't think that you are immature or weak at math.
@@varfarrog4544 also ln(x) where x is negative is NOT undefined. It is a complex number. For example
ln(-1)=3.1415i (approx)
Answer is 5i
5i is correct, \/16 = +- 4
I always thought (-3 * -3) and (-3^2) were the same.
(-3×-3)=(-3)²
(-3²)=-3×-3
@@mrhtutoring ???
@@ugonnahart3908
-3^2
and
(-3)^2
are different because the one without paranthesis is only applying to the 3, not the negative, while the one with paranthesis is applying to the negative AND 3
-3^2=-1(3^2)=(-1)(9)
(-3)^2=(-1)^2 (3)^2=(1)(9)
@@naopoint4096 thank you. As always, the position of the parenthesis matters.
I figure it to be 5i....
So, to be clear: [ --9^2 = --81]; [ --(9^2) = --81]; [(--9)^2 = +81]; --(--9^2) = +81.....
Answer is B
-5^2 = -25
sqrt(-25) = 5i
C.-5
Here I thought multiplying two negatives equals a positive
A minus ain't squared, unless it's been snared.
In this case, the -5 isn't squared together, when written as -5^2. Only the 5 is squared. The minus is applied after the squaring.
Since it is so much more common that you prefer signs to be applied after exponents, it is convention that you have to snare your negative signs, if you want them raised to any power. Thus, you'd have to write it as sqrt((-5)^2), if you wanted two negatives to multiply to be a positive in an example similar to the given one.
it does but -a²=-(a²)
I came up with b
I checked WolframAlpha to see what it said about -3^2. Its answer was -9.
That's the way to go!
@@mrhtutoring: I’m a bit confused as well . There was an example of : If x = -3 , then what is x^2 . And your answer was 9, not -9 . And now you have this -3^2 is -9 .
When x=-3, x²=(-3)²=9
But when you have -3², it's equal to -9.
The right answer is b
what about the left one?
@@alexbarbucristi this thing you did should be illegal,🚷🔞
It -5
√-5² = √-25 = 5i
+-5i
It is b, 5i.
(b) √-5^2 = √-25 = i√25 = 5i
-5²=-25
√-25=5i
The correct answer is (b)
Oh yeah. Got it right.
√(-5²)
√(-1 × 5²)
√(-1) × √(5²)
i × 5
5i
Who would disagree that 4 is the square root of 16?
Some people say +-4 since -4 x -4 =16
What is the value of “i’
i is the square root of -1, also known as the imaginary unit. This isn't a real number, so we can't reduce it any further than i.
Don't let the name deceive you, just because we call it imaginary. That was just a name coined by a critic, that somehow stood the test of time, when people first came up with the idea of imaginary numbers. There are plenty of practical applications of these numbers
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