SOLUTION: Rationalize the denominator: 2-√(7) divided by √(3) - √(2) In the examples I have I believe I am supposed to multiply the numberator and denominator by the den

Algebra ->  Square-cubic-other-roots -> SOLUTION: Rationalize the denominator: 2-√(7) divided by √(3) - √(2) In the examples I have I believe I am supposed to multiply the numberator and denominator by the den      Log On


   

Question 251889: Rationalize the denominator: 2-√(7) divided by √(3) - √(2)
In the examples I have I believe I am supposed to multiply the numberator and denominator by the denominator....is this the correct way to start this equation or am I missing something.
I have read through the lessons and I am still very confused. If someone could show me the steps I would greatly appreciate it as maybe then I could wrap my brain around this.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


You cannot simply multiply by the denominator because that would square the denominator. If you square the denominator, you would still have radicals in the denominator.

Let's say that either or (or both) are the square root of an integer. Then, in general



would still be irrational because while the the two 2nd power terms would be rational, the 2ab term in the middle would still be irrational -- and squaring it again would just make things worse.

However, recall the difference of two squares factorization:



So, given a binomial expression in the denominator where at least one of the factors of the binomial is an irrational square root, you need to multiply the entire fraction by 1 in the form of the CONJUGATE of the denominator divided by itself. Form the conjugate of a binomial by simply changing the sign in the middle, that is: is the conjugate of (and vice versa, of course).


John