Like what you saw?
Create FREE Account and:
 Watch all FREE content in 21 subjects(388 videos for 23 hours)
 FREE advice on how to get better grades at school from an expert
 Attend and watch FREE live webinar on useful topics
Rationalizing a Denominator with a Binomial  Concept
Carl Horowitz
Carl Horowitz
University of Michigan
Runs his own tutoring company
Carl taught upperlevel math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!
When rationalizing a denominator with two terms, called a binomial, first identify the conjugate of the binomial. The conjugate is the same binomial except the second term has an opposite sign. Next, multiply the numerator and denominator by the conjugate. The denominator becomes a difference of squares, which will eliminate the square roots in the denominator.
Rationalizing the denominator with a binomial with 2 terms in the denominator. So for this example what we're looking at 3 over 1 plus root 3, and we want to rationalize the denominator. We want to get rid of that square root in the denominator.
What we're used to doing is just multiplying by the square root that we have, okay. So what I mean by that is if we multiply this by root 3 over root 3, what actually ends up happening is this root 3 gets distributed into both things, so we end up with root 3 plus root 3 times root 3 which is just going to be 3. We haven't actually gotten rid of our square root at all. All we've done is move the square root from one term to the other and made our terms bigger, okay? So this isn't going to work.
What we actually have to do is multiply by something else, and that something else is called the conjugate which is basically the same numbers but the opposite sign in between. So that in this case is going to be one minus root 3 over one minus root 3, it has to be multiplied by 1. And what happens is now when we multiply this through we have to foil it out and so we end up with 1. We have positive root 3 and negative root 3 which cancel, so those disappear and then we have root 3 times root 3 which is 3. This should be our negative. So we end up with 13 in the denominator or 2 which is what we wanted. We wanted to get rid of that negative sign from the denominator. Okay?
We still have to distribute this 3 in the numerator. So we end up with 33 root 3 all over 2. Okay?
So when we're multiplying, sorry. In order to get rid of the square root from the denominator when we have two terms, we have to multiply by the conjugate which is the same thing but just with a different sign in between.
Please enter your name.
Are you sure you want to delete this comment?
Carl Horowitz
B.S. in Mathematics University of Michigan
He knows how to make difficult math concepts easy for everyone to understand. He speaks at a steady pace and his stepbystep explanations are easy to follow.
i love you you are the best, ive spent 3 hours trying to understand probability and this is making sense now finally”
BRIGHTSTORM IS A REVOLUTION !!!”
because of you i ve got a 100/100 in my test thanks”
Sample Problems (8)
Need help with a problem?
Watch expert teachers solve similar problems.

Rationalizing a Denominator with a Binomial
Problem 1 3,425 viewsRationalizing the denominator:
3 2  √5 
Rationalizing a Denominator with a Binomial
Problem 2 3,062 viewsRationalizing the denominator.
√3 √5 + √2 
Rationalizing a Denominator with a Binomial
Problem 3 562 views 
Rationalizing a Denominator with a Binomial
Problem 4 603 views 
Rationalizing a Denominator with a Binomial
Problem 5 546 views 
Rationalizing a Denominator with a Binomial
Problem 6 530 views 
Rationalizing a Denominator with a Binomial
Problem 7 531 views 
Rationalizing a Denominator with a Binomial
Problem 8 564 views
Comments (0)
Please Sign in or Sign up to add your comment.
·
Delete