2 over (2 + square root of 3) =? many are going to get this WRONG!
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- เผยแพร่เมื่อ 8 มี.ค. 2024
- How to rationalize the denominator with conjugate. Learn more math at TCMathAcademy.com/.
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Thank you for waking up my mind. Now 75yrs. I tutored math while studying to be an RN to Viet Nam vets. Then helping home schooled family members two generations. I have always loved math thanks again
D) 4-2sqrt3
This concept of not dividing by an irrational number has always bothered me because multiplying by such seems to be just fine. When you think about, we use other things that don’t make sense in a concrete way either: like 6^2.5. How can you physically have something multiplied by itself 2.5 times?
You're absolutely right. There is no problem dividing by irrational numbers at all.
Looking at the thumbnail image for the video he has the initial expression 2/(2+√3) and then 4 multiple choice answers. If he restricted himself to posing the question as "which of these four options is equivalent to the original expression?" then the question would be fine. But he insists on trying to present irrational numbers in denominators as somehow a bad thing when they really aren't an issue at all.
got it D multiply by the recip and expand. thanks for the fun.
It’s D. Multiply top and bottom by 2 - sqrt(3).
d) 4-2sqr(3)
I'm actually following you,but will have to go over this a few times ( or maybe many😅, but I'm following you)
Trig identifies have been whooping my butt. Been learning a lot about conjugates
d.)4-2sqrt3
It's clear that multiplying denominator by its conjugate gives 1. So rationalizing denominator, we get
2 * conjugate of denominator / 1 = 2(2−√3) = 4−2√3
But since this is a multiple choice, we could always just eliminate wrong answers.
(a) and (b) are clearly wrong. We cannot end up with fractions of the form a/√b or √a/b from the original number.
Also, we can see rather quickly that 2/(2+√3) = 1/(1+0.5√3) which is not equal to 1/(1+√3), so we can also eliminate (c).
This leaves (d) 4−2√3
First of all can’t have a radical in the denominator so that eliminates A and C
Of course you can have a radical in the denominator. There's one right there in the question. You can't eliminate A and C as candidates just on that basis.
Hi. It´s Celso here, from Brazil. Thank you, guy, 'coz now I can join my study of English with ... Maths! Hugs.
Thanks, but I need to use this “simplified” problem several times before it sinks in. Believe it or not I had a couple of things right before going off the rails with the variable. Plus 25 someone became ❤2 x2x5 as the mind choked.
Thank you
I am an expert in algebra and answer all your videos in my head except this one. I already knew you can't multiply the top and bottom by the sqrt(3). I tried squaring the top and bottom but that didn't resolve the issue either. It is 3am in the morning and could not come up with the conjugate of the denominator. Once I saw the (2 -sqrt(3)), I instantly could see the denominator was one in my head. My bad but maybe my age of 73 and the late night slowed me down a little. My only redemption is that my guess was the answer "D" or 4 - sqrt(3) but I cheated and used a calculator.
Good math teacher just learnt something that was dificult to learn in scool
d) 4-2√3
Hi, do you tutor for Calculas for university level?
I can't make sense out of that. 2+square root of 3=3.732. 2÷3.732=0.536. It's a straightforward problem.
I aced algebra in high school and never used it again! I do know the square root of PI!
No one should think they can't do math! Many math teachers are very poor (unfortunately). In my experience.
In high school, I realized all my math teachers were competent; years later, I realized the later math teachers were highly verbal over a condensed symbolic system. I.e., we hire lawyers who do their legal system for us. Or a football diagram, for example, of a play uses its own symbolic system to convey an outcome.
Looking at the thumbnail for 3 seconds: Rationalising the denominator gives you 4-3=1, which leaves thenumerator as 2(2-sqrt(3)) or 4-2sqrt(3), which is answer Dy
If I was in the class I would ask why my fancy "one" is not 2 + square root of 3 OVER itself.
In other words how can I see that I need to use the conjugate and change the plus for a minus?
After all, both values are equal to one whether I keep it as it is or change it for a substraction.
What am I missing?
The idea in most problems like this is to rationalize the denominator.
Recall that (a+b)(a−b) = a² − b² while (a+b)(a+b) = a²+2ab+b²
Since denominator is in the form a+√c (where a and c are integers),
then multiplying denominator by a−√c gives a²−(√c)² = a²−c, which is an integer.
But multiplying denominator by a+√c gives a²+2a√c + (√c)² = (a²+c)+(2a)√c,
which is still in the form m+n√c, (with m and n being integers), which is still not rational.
Since denominator 2+√3 needs to be multiplied by 2−√3 to rationalize denominator,
we multiply the whole fraction by (2−√3)/(2−√3)
Now you might point out to answer (c) = 1/(1+√3) which does not have a rational denominator. But there are two ways to quickly determine that this is not equal to 2/(2+√3).
First, 1/(1+√3) = 2/(2+2√3) which is clearly not = 2/(2+√3) since both numbers have same numerator, but different denominators.
Second, the denominator (1+√3) cannot be obtained by multiplying or dividing original denominator (2+√3) by an integer or rational number, not can it be obtained by multiplying or dividing (2+√3) by an irrational number of the form √b. So it can only be obtained by multiplying by an irrational number of the form (a+√b), which will result in a numerator of the form 2(a+√b) which cannot be simplified to 1.
We can also eliminate answers (a) 1/√3 and (b) √3/4 since a number of the form a/(b+√c) never simplifies to the form m/√n or √m/n (where a,b,c,m,m are all integers)
@@MarieAnne. Thank you! I'll keep this in my notes. :)
Thank you many times over.
d) 4 - 2\/3
Good evening everyone.
How are you .
I'm 56 and want to keep my mind and in good shape. That's the only reason I'm doing some math drills. My main issue is the handwriting especially in math. I'm cerebral palsy since birth, The reason I'm making mistakes, is because my handwriting is not staight and all " tangled "
My question, is there a software for algebra or Geometry . Could I work math on word
Thahks everyone.
17:06 but WHY did you have to go for a long and boring way? That was a formula for you to grab: (a-b)(a+b) = a² - b²
It took nearly 50 seconds to say the answer was d and praising for the correct answer.
This time I took a guess and guessed right. But I needed the tutorial to know what to do. I was on the right track but got stuck in the mud after the first step. :(
I need to understand the process
D
I got D, but I multiplied by (-2+sqr3)
(2+V3) . (2-V3) will do the trick.
I am not student, I just remember for twenty years to understand that, correct my information.🇰🇼✅✅✅💯💯👍👍👍
Easy, Opt (d)
So, it"s about factoring, is'n't it ?
Very easy
Or thirty years, I interesting it.
d
Do I spot a mistake?
I think you need to be more specific if you do.
Yes, you do.
Sqrt 9 is also -3, which yields (4-2sqrt3)/5.
@@AD12086 Sqrt 9 is shown as being derived from Sqrt 3 x Sqrt 3 which is 3 not -3. Besides,
x^2 = 25, x = +/-5 BUT, Sqrt(25) always equals 5
A so complicate way to say that you have to multiply the denominator by 1 . Why using the word " conjugate "
d. Because I am dumb
Way too long for such a simple problem.
No bone for you today. Come back one year.
Too long. Cut to the chase!
So D is the answer. Why is right. Why does algebra have to be donei with all the mental gymnastics? What HONEST every day application does it suit anyone except possibly a rocket engineer. Come on🤷
I can't pay attention to one problem for 20 minutes. It would be more helpful if you could get to the point before I stop caring and start daydreaming. A problem like this should be explained in 5 or 6 minutes tops. You don't have to keep repeating yourself. The beauty of teaching on video is that people can rewatch it if they need to.
Agreed, but the longer a video is, that gets watched to the end by multiple people, the more money the channel gets.
It's all about the bucks.
You should just skip ahead to the answer next time. No sense wasting all that untapped intellect actually learning 'why things are done' in addition to 'how things are done'.
Better yet... just round up or down to numbers that you feel comfortable working with - estimate the answers.
You’re not very grateful. This instructor does not own you the time to listen to your complaints!
@@throngcleaverhow rude. Who do you think you are, who cares what you have to say. All you complainers, ungrateful know it all don’t have to watch the video
@@suefuller3014 You should stop whining and learn how the world works.
In your videos you repeatedly refer to "cancel" or "cancel out". There is no mathematic or arithmetic operation as cancel! Terms either "zero out" - meaning their sums equal zero, or the product of multiplication results in an identity; a number divided by itself.
Please stop confusing students with "CANCEL" unless you are referring to a social phenomenon. The arithmetic operations are Addition, Subtraction, Multiplication, and Division. Express yourself with one of these four operations.
You are taking it too long, 20 min video is excessive for this problem.
You're an adult clearly, These problems are for school-aged children who are learning.
0.535898
A
All this character wants to do is confuse people so we all keep coming back and watch the adverts.
You too much talk it should be less talking so that your viewers don't get sleepy. Try to get lesson from indians they more comprehensive than yours.
D
d
D
D