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
Think about (a + b)(a - b) = a^2 - b^2 to get rid of the root in the denominator. So multiply numerator and denominator by (2 - sqr.rt. 3). Then you get 4 - 2 x sqr.rt 3/1 which is 4 - 2 x sqr. rt. 3.
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
This guy's videos can be helpful. However, his detailed explanations can sometimes be confusing, because they go off at tangents sometimes. This interruption in flow and concentration on unimportant points can work against gaining a clear understanding of the subject.
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.
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.
Looked at it, decided to multiply by an identity that eliminated the radical in the denominator i.e. 2-root(3). That leaves only whole numbers in the denominator and ans. D.
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.
I think the method you used here man is better suited to Algebra because , 2/ 2+ square root of 3 is equal to 2/ 3.7320508…..= 0.5358984 Your final answer using your method ,…..4- ( 2x square root of 3) 4- 3.4641016 = 0.5358984 In your original question the two numbers in the denominator should have been put in brackets as that is the number that 2 is going to be divided by . Thanks for sharing …….remember……” force = mass x acceleration “
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.
Is it a language issue? You can have 6^2 • 6^0.5 I'm sure you'd accept the 0.5 there? And the whole expression is the same as 6^2.5 But anyway I once lived in a flat with an irrational person living in the flat below me. I wasn't comfortable as the numerator in that situation.
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.
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
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.
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)
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 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.
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.
@@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
I agree you're boring us, on these tangents. But maybe, if you were more excited, your extra explanations would be cool. But i can't stay long enough to get to the end.
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🤷
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.
I got the right answer, but it was obvious that A, B and C are wrong..... I did not actually go thru the steps to verify that D is correct. It is nice that he is publishing these videos. But this guy is very slow and boring. He could have explained this in less than 5 mins instead of a 20 min video. I lost interest after about 5 mins.
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
Think about (a + b)(a - b) = a^2 - b^2 to get rid of the root in the denominator. So multiply numerator and denominator by (2 - sqr.rt. 3). Then you get 4 - 2 x sqr.rt 3/1 which is 4 - 2 x sqr. rt. 3.
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
D) 4-2sqrt3
Hi. It´s Celso here, from Brazil. Thank you, guy, 'coz now I can join my study of English with ... Maths! Hugs.
d.)4-2sqrt3
Trig identifies have been whooping my butt. Been learning a lot about conjugates
This guy's videos can be helpful. However, his detailed explanations can sometimes be confusing, because they go off at tangents sometimes. This interruption in flow and concentration on unimportant points can work against gaining a clear understanding of the subject.
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.
d) 4-2sqr(3)
It’s D. Multiply top and bottom by 2 - sqrt(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.
got it D multiply by the recip and expand. thanks for the fun.
I saw the correct answer in my head, so my brain must have done that sequence of operations automatically. That's quite worrying.
Invert denominator and multiply by numerator but don't forget to change the sign of the inverted denominator first !
Looked at it, decided to multiply by an identity that eliminated the radical in the denominator i.e. 2-root(3). That leaves only whole numbers in the denominator and ans. D.
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.
I multiplied the numerator and denominator by 2 - root3, so arrived at 2(2 - root3)/(4 - 3), so resulted in 2(2 - root3) or (d)
I think the method you used here man is better suited to Algebra because , 2/ 2+ square root of 3 is equal to 2/ 3.7320508…..= 0.5358984
Your final answer using your method ,…..4- ( 2x square root of 3)
4- 3.4641016 = 0.5358984
In your original question the two numbers in the denominator should have been put in brackets as that is the number that 2 is going to be divided by .
Thanks for sharing …….remember……” force = mass x acceleration “
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.
Is it a language issue? You can have 6^2 • 6^0.5 I'm sure you'd accept the 0.5 there? And the whole expression is the same as 6^2.5 But anyway I once lived in a flat with an irrational person living in the flat below me. I wasn't comfortable as the numerator in that situation.
I aced algebra in high school and never used it again! I do know the square root of PI!
Hi, do you tutor for Calculas for university level?
d) 4-2√3
I'm actually following you,but will have to go over this a few times ( or maybe many😅, but I'm following you)
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.
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
Good math teacher just learnt something that was dificult to learn in scool
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.
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.
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! I selected D.
Move it along! Skip to 8:50 to start, or even 15:00
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. :(
d) 4 - 2\/3
(2+V3) . (2-V3) will do the trick.
I save some of your videos so I can review until learn how to work certain problems.
3'14
Thank you
3-14+😮2=6'28-
I am not student, I just remember for twenty years to understand that, correct my information.🇰🇼✅✅✅💯💯👍👍👍
Thank you many times over.
Interesting and important content. But it’s very long and repetitive. It would be far more effective if it were 5 minutes long.
I need to understand the process
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.
Now this one is easy. Not just because a and c are not valid as answers.
I got D, but I multiplied by (-2+sqr3)
It took nearly 50 seconds to say the answer was d and praising for the correct answer.
So, it"s about factoring, is'n't it ?
C
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
Too long. Cut to the chase!
Way too long for such a simple problem.
Easy, Opt (d)
C is my answer
D is your answer
D
d
Very easy
I agree you're boring us, on these tangents. But maybe, if you were more excited, your extra explanations would be cool. But i can't stay long enough to get to the end.
Or thirty years, I interesting it.
A so complicate way to say that you have to multiply the denominator by 1 . Why using the word " conjugate "
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🤷
making a full video from one simple equation.😅
d. Because I am dumb
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
Blaming the student is not good practice.
Very confusing
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.
No bone for you today. Come back one year.
Doesn’t require 20 mins to explain this, surely?
It's a math class. 20 minutes is perfect.
I got the right answer, but it was obvious that A, B and C are wrong..... I did not actually go thru the steps to verify that D is correct. It is nice that he is publishing these videos. But this guy is very slow and boring. He could have explained this in less than 5 mins instead of a 20 min video. I lost interest after about 5 mins.
Why don’t you listen to everyone instead of doing what you want and STOP TALKING SO MUCH AND SOLVE THE PROBLEM.
It is EXTREMELY ANNOYING !
A
0.535898
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.
All this character wants to do is confuse people so we all keep coming back and watch the adverts.
d
A
D
D
A
D
D