Rationalize the denominator

**Cuelguy** · June 29th 2009, 05:28 AM

I need help with this:

Rationalize the denominator:

Thanks in advance

**pfarnall** · June 29th 2009, 05:37 AM

Originally Posted by Cuelguy

I need help with this:

Rationalize the denominator:

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

Thanks in advance.

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

**Cuelguy** · June 29th 2009, 05:45 AM

Originally Posted by pfarnall

Are you familiar with "the difference of two squares", basically it says that:
$a^2-b^2=(a-b)(a+b)$
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) ?

**pfarnall** · June 29th 2009, 05:49 AM

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!

**Cuelguy** · June 29th 2009, 05:58 AM

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.

**skeeter** · June 29th 2009, 06:19 AM

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

**pfarnall** · June 29th 2009, 07:48 AM

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

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