1. ## Rationalize the denominator

I need help with this:

Rationalize the denominator:

2. Originally Posted by Cuelguy
I need help with this:

Rationalize the denominator:

$\displaystyle sqrt{6}+sqrt{5}/sqrt{6}-sqrt{5}$

Are you familiar with "the difference of two squares", basically it says that:
$\displaystyle a^2-b^2=(a-b)(a+b)$
now with this in mind think about what you might like to multiply the numerator and denominator of your fraction by...

3. Originally Posted by pfarnall
Are you familiar with "the difference of two squares", basically it says that:
$\displaystyle a^2-b^2=(a-b)(a+b)$
now with this in mind think about what you might like to multiply the numerator and denominator of your fraction by...
....the conjugate of the denominator, correct?

So I would multiply the numerator and denominator by sqrt(6) + sqrt(5) ?

4. Originally Posted by Cuelguy
....the conjugate of the denominator, correct?

So I would multiply the numerator and denominator by sqrt(6) + sqrt(5) ?
Spot on! Well done, and the formula I gave you means you don't even have to work out what the new denominator will be, it's already there for you!

5. Originally Posted by pfarnall
Spot on! Well done, and the formula I gave you means you don't even have to work out what the new denominator will be, it's already there for you!
Okay here is what I got as a final answer after collecting all the like terms, but the answer is still wrong. I am pretty sure it's because of the square root of 5 & 6 in my answer below....I don't know how to combine them.

6. $\displaystyle \frac{\sqrt{6}+\sqrt{5}}{\sqrt{6}-\sqrt{5}} \cdot \frac{\sqrt{6}+\sqrt{5}}{\sqrt{6}+\sqrt{5}} = \frac{6 + 2\sqrt{30} + 5}{6 - 5} = 11 + 2\sqrt{30}$

7. Yes you had it all, you just need to learn that $\displaystyle \sqrt{a}\sqrt{b}=\sqrt{ab}$ (also that 6-5=1 but I'm sure you know that already)