SQRT(8)/ SQRT(3) = SQRT(8/3) = SQRT ( 4 x 2/3) = 2 x SQRT (2/3) If you prefer no fractions under the SQRT sign: = 2 x SQRT ((2/3)x (3/3)) = 2 x SQRT(6)/ 3
I did not do math since I was 19..... I am 74 now.... I knew that radical of 3 was irrational.... ha, ha, like a lot of decimals. I also knew that I had to change the form of the fraction.... some kind of deconstruction....if I can say that. But thank you; I am doing this to keep my mind occupied.
√8 : √3 -- Fraction_Form -- √[8/3] Get the root out of the denominator (rationalize the denominator) : √{[8 x 3]/[3 x 3]} √{[8 x 3]/[3 x 3]} = √24 / √9 = √[24] / 3 ✔ let's break it down further: all the squares less than 24. 0² = 0 , 1² = 1 , 2² = 4 , 3² = 9 , 4²=16 , 5² > 24 2² x 6 = 24 √[2² x 6] / 3 = 2√6 / 3 ☑
To divide a pizza by PI slice in a decending radius that approaches the center by half the distance of the previous rotation. Simply slice eqaul weight pieces when you never reach the center:).
super simple I will rewrite this as a multiplication problem using a negative exponent to represent reciprocal. (8 ^ 1/2) * (3 ^ -1/2) you cant have an irrational denominator so we will rationalize it by multiplying the numerator and denominator by (3 ^ 1/2) numerator: (8 ^ 1/2) * (3 ^ 1/2) (8 * 3) ^ 1/2 (24) ^ 1/2 or (6 * 4) ^ 1/2 2(6)^1/2 Denominator: (3 ^ 1/2) * (3 ^ 1/2) or (3 * 3) ^ 1/2 9^ 1/2 = 3 This gives us the final answer [ 2(6 ^ 1/2) ] divided by 3 [ ] used to show everything is over 3. When you have a fraction as an exponent, the numerator represents the power and the denominator represents the root. So square root of x is x ^ 1/2. By introducing negative one to the exponent we are saying it is the reciprocal of it. Example x ^ -1 means 1 divided by x.
In my 60's too and a retired engineer. I stopped at 2*sqrt(2/3) because I forgot the rule (tradition?) of removing irrationals from the denominator. But continued, 2/3 is 0.666 etc, and not wanting to spend eternity in hell, I thought that was close to 0.64, which is a perfect square, so an approx answer is 2 * 0.8 or 1.6. Removing irrationals from the denominator is an ancient tradition from back when the most sophisticated computing power was a slide rule. These days I'm not so sure that is needed, is it?
In another video John tries to explain it, by saying imagine slicing a pizza into π slices, or √10 slices. If you were selling the slices your customer wouldn't be satisfied. So maybe it's all about cust. satisfac.
Root 8 divided by root 3? Well, you multiply the numerator and denominator by root 3 to get the radical out of the denominator. You have root 24 divided by 3, which simplifies to … (2*sqrt(6))/3 Adding due to prompts after solution given: -In general, radicals need to be removed from denominators because the square root of any number that is not a square number (1, 4, 9, etc.) is an irrational number, which cannot be represented as a fraction and is going to appear as an unending series of digits. Since we need to divide by the denominator, this is a problem. In this case, if you multiply the denominator by itself, you get a nice whole number, but you must do the same to the numerator to maintain the value of the original prompt. -The issue with the numerator is that, while radicals are allowed here, we should get whatever we can get out from under the radical. If you do this to sqrt(8), you can get sqrt(4*2), which means we can take the 4 out of the radical by taking it’s square root, which is 2. So sqrt(8) simplifies to 2*sqrt(2). Multiplying by sqrt(3) gives 2*sqrt(2)*sqrt(3), which can be combined into 2*sqrt(2*3), which is 2*sqrt(6). I actually multiplied by sqrt(3) first, then simplified. This gets you sqrt(8)*sqrt(3), which is sqrt(8*3), or sqrt(24). 24 can be expressed as 4*6, and we again pull out the 4 to end up with 2*sqrt(6).
Don't worry. There's no problem with radicals in denominators. It's completely normal. The number is still irrational whether you write it as 2√(2/3) or (2√6)/3. It's purely a stylistic choice. Mathematics doesn't care about radicals in denominators.
when watching your video's I have a habit of saying 'oh yes that's completely obvious' at each step, having sat staring and thinking for several minutes.
You seem a nice guy but your verbosity detracts from the lesson. Perhaps give the short track lesson and then follow with the explanation. I lose the will to live after 5 minutes and i love maths. 😂
I don't understand... how is your answer any different from the first expression. They are both mathematical expressions whereas the answer in my view is rounded to 2 decimal points 1.63 I need help to understand how an answer to a mathematical equation can simply be another mathematical equation that doesn't put you any closer to knowing the numeric answer...? P.S I love Math but I didn't study hard enough when young... I'm now retired and am having fun going to back to Math and having another go.
This video should be 3 minutes long without all the smiley face BS. Why do you turn this into a freakin 15 minute video??? Same with all your videos. I would love reviewing these math problems but not a FN 15 minute video!!!! Gerrr
I'm just amazed at how much mathematics I still know at 63.
This is a great mental workout.
SQRT(8)/ SQRT(3)
= SQRT(8/3)
= SQRT ( 4 x 2/3)
= 2 x SQRT (2/3)
If you prefer no fractions under the SQRT sign:
= 2 x SQRT ((2/3)x (3/3))
= 2 x SQRT(6)/ 3
That's pretty fancy, dude! 🙂👌
We need a lot of patience to see your videos!! … ¡uff!!
I did not do math since I was 19..... I am 74 now.... I knew that radical of 3 was irrational.... ha, ha, like a lot of decimals. I also knew that I had to change the form of the fraction.... some kind of deconstruction....if I can say that. But thank you; I am doing this to keep my mind occupied.
@@michellen2325 most ALL.of us do this to occupy our aging minds
Have you tried Sudoku?
Or the chess of Fischer?
√8 : √3 -- Fraction_Form -- √[8/3]
Get the root out of the denominator (rationalize the denominator) : √{[8 x 3]/[3 x 3]}
√{[8 x 3]/[3 x 3]} = √24 / √9 = √[24] / 3 ✔
let's break it down further: all the squares less than 24.
0² = 0 , 1² = 1 , 2² = 4 , 3² = 9 , 4²=16 , 5² > 24
2² x 6 = 24
√[2² x 6] / 3 = 2√6 / 3 ☑
You should be a math tutor!
Maybe John has too many pupils and he can use some help!
Got it.
Multiply by sr 3
Get sr 24 / 3
sr 24 =
sr 4 x sr 6
That = (2 sr 6) / 3
Thanks for the fun
Enjoyed this. Thank you.
You could have simply said rationalize the denominator. but i like your approach
How would you rationalize it
@@blueman-z1mThat's what he's doing in the video. He wants to not have a √ in the denominator.
FFS , just square both sides. After that it's just simple division.
14:37 This is the key to earning an "A" in any class, but especially in Mathematics class.
To divide a pizza by PI slice in a decending radius that approaches the center by half the distance of the previous rotation. Simply slice eqaul weight pieces when you never reach the center:).
super simple I will rewrite this as a multiplication problem using a negative exponent to represent reciprocal.
(8 ^ 1/2) * (3 ^ -1/2)
you cant have an irrational denominator so we will rationalize it by multiplying the numerator and denominator by (3 ^ 1/2)
numerator:
(8 ^ 1/2) * (3 ^ 1/2)
(8 * 3) ^ 1/2
(24) ^ 1/2 or (6 * 4) ^ 1/2
2(6)^1/2
Denominator:
(3 ^ 1/2) * (3 ^ 1/2) or (3 * 3) ^ 1/2
9^ 1/2 = 3
This gives us the final answer
[ 2(6 ^ 1/2) ] divided by 3
[ ] used to show everything is over 3. When you have a fraction as an exponent, the numerator represents the power and the denominator represents the root. So square root of x is x ^ 1/2. By introducing negative one to the exponent we are saying it is the reciprocal of it. Example x ^ -1 means 1 divided by x.
Wow this was really good stuff Mathman . I'm addicted to math, I have a serious math problem 😂
Thanks Mr J 👍🙏👏💪😎🌎
Could be worse.
There is nothing to “solve” since there is no equation. Math language is precise.
Good point.
Apparently language is a different department.
(2√6)/3 Yes
√8/√3 = (√8 •√3) / (√3 • √3)
= 2√(2•3) / 3 = 2 √6 / 3
I can’t see that this is ‘solving’ anything. At best it’s rearranging or simplifying.
That was fun! I got it wrong and enjoyed the 'splain!! Thank you!
What is the name of the whiteboard software?
Chalk
@@thenetsurferboy cheers
Multiply Num & Denom by Sqrt 3... then Demon is 3, and Num becomes Sqrt (8*3) which is 2 Sqrt 6. So, the ans is (2 Sqrt 6)/3.
In my 60's too and a retired engineer. I stopped at 2*sqrt(2/3) because I forgot the rule (tradition?) of removing irrationals from the denominator. But continued, 2/3 is 0.666 etc, and not wanting to spend eternity in hell, I thought that was close to 0.64, which is a perfect square, so an approx answer is 2 * 0.8 or 1.6.
Removing irrationals from the denominator is an ancient tradition from back when the most sophisticated computing power was a slide rule. These days I'm not so sure that is needed, is it?
You should never forget basic year 9 surds like that
In another video John tries to explain it, by saying imagine slicing a pizza into π slices, or √10 slices. If you were selling the slices your customer wouldn't be satisfied. So maybe it's all about cust. satisfac.
V8 = 2V2 so V8 / V3 = 2V2 . V3 / V3 . V3 = 2V6 / 3
Why would you not approximately 1.632?
sqrt(8)÷sqrt(3)
gotta get rid of sqrt in denominator, so
sqrt(3)/sqrt(3)×(sqrt8/3)
= sqrt(8)sqrt(3)/3
= (2sqrt(2)sqrt(3))/3
= (2/3)sqrt(6)
Wanna, not gotta.
Yay I got one right 😊 but it's an ugly answer, I'd prefer it came out to 3/2
(√8 / √3) × (√3 / √3)
= √24 / 3
= (√4 × √6)/3
= (2 × √6)/3
√8 ÷ √3 = √4 · √2 ÷ √3 = 2 · √2 ÷ √3 = 2 · √2 · √3 ÷ √3 · √3 = 2 · √6 ÷ 3
You just complicated an easy problem by adding too many unnecessary steps.
2 sq.root of 6/3
1.63299
2squre root 2/3
(✓8)/(✓3) = [(✓8)(✓3)]/[(✓3)(✓3)] = (✓24)/3 = (2✓6)/3
I forgot sqrt (2) x sqrt(3) can be written sqrt(6), but I got the rest of the answer right. Can I have a B or B-plus, maybe, pretty please?
Root 8 divided by root 3? Well, you multiply the numerator and denominator by root 3 to get the radical out of the denominator. You have root 24 divided by 3, which simplifies to …
(2*sqrt(6))/3
Adding due to prompts after solution given:
-In general, radicals need to be removed from denominators because the square root of any number that is not a square number (1, 4, 9, etc.) is an irrational number, which cannot be represented as a fraction and is going to appear as an unending series of digits. Since we need to divide by the denominator, this is a problem. In this case, if you multiply the denominator by itself, you get a nice whole number, but you must do the same to the numerator to maintain the value of the original prompt.
-The issue with the numerator is that, while radicals are allowed here, we should get whatever we can get out from under the radical. If you do this to sqrt(8), you can get sqrt(4*2), which means we can take the 4 out of the radical by taking it’s square root, which is 2. So sqrt(8) simplifies to 2*sqrt(2). Multiplying by sqrt(3) gives 2*sqrt(2)*sqrt(3), which can be combined into 2*sqrt(2*3), which is 2*sqrt(6).
I actually multiplied by sqrt(3) first, then simplified. This gets you sqrt(8)*sqrt(3), which is sqrt(8*3), or sqrt(24). 24 can be expressed as 4*6, and we again pull out the 4 to end up with 2*sqrt(6).
Don't worry. There's no problem with radicals in denominators. It's completely normal.
The number is still irrational whether you write it as 2√(2/3) or (2√6)/3.
It's purely a stylistic choice. Mathematics doesn't care about radicals in denominators.
I am the dire need in algebra/calc/trig
when watching your video's I have a habit of saying 'oh yes that's completely obvious' at each step,
having sat staring and thinking for several minutes.
You seem a nice guy but your verbosity detracts from the lesson. Perhaps give the short track lesson and then follow with the explanation.
I lose the will to live after 5 minutes and i love maths. 😂
I don't understand... how is your answer any different from the first expression.
They are both mathematical expressions whereas the answer in my view is rounded to 2 decimal points 1.63
I need help to understand how an answer to a mathematical equation can simply be another mathematical equation that doesn't put you any closer to knowing the numeric answer...?
P.S
I love Math but I didn't study hard enough when young... I'm now retired and am having fun going to back to Math and having another go.
do you mean ... simplify as I do not see a variable so there is nothing to solve .... :)
Non math person...just feel that i dont have a final answer without laborious pen and paper calculation of sq root of 6.
This video should be 3 minutes long without all the smiley face BS. Why do you turn this into a freakin 15 minute video??? Same with all your videos. I would love reviewing these math problems but not a FN 15 minute video!!!! Gerrr
be thankful it is only 15 minutes. I feel he did a rush job on this one.
You lost me !