• Aug 11th 2008, 07:41 AM
mommyneedshelp
I am trying to help my daughter with this problem

2+square root of 5 over 3 - square root of 6. Please come to my rescue!
• Aug 11th 2008, 07:45 AM
skeeter
have your daughter multiply numerator and denominator by

$3 + \sqrt{6}$

then simplify.
• Aug 11th 2008, 07:47 AM
mommyneedshelp
Not 3-square root of 6?
• Aug 11th 2008, 07:51 AM
Simplicity
Quote:

Originally Posted by mommyneedshelp
I am trying to help my daughter with this problem

2+square root of 5 over 3 - square root of 6. Please come to my rescue!

In a fraction, you do not keep a surd ( $\sqrt{x}$) on the denominator so when it says to simplify the expression, your aim is to remove the surd from the denominator.

$\frac{2+\sqrt{5}}{3-\sqrt{6}}$

Multiply the numerator and the denominator by the conjugate of the denominator which is $3+\sqrt{6}$

$\left(\frac{2+\sqrt{5}}{3-\sqrt{6}}\right)\left(\frac{3+\sqrt{6}}{3+\sqrt{6} }\right)$

Multiply all the expressions. Numerator with numerator and denominator with denominator.

$=\frac{6 + 2\sqrt{6} + 3\sqrt{5} +\sqrt{30}}{9 + 3\sqrt{6} - 3\sqrt{6} -6}$

$=\frac{6 + 2\sqrt{6} + 3\sqrt{5} +\sqrt{30}}{3}$
• Aug 11th 2008, 08:31 AM
mommyneedshelp
Thank you so much for your help!