# How do you simplify (sqrt5+2sqrt2)/(4-sqrt5)?

Jan 15, 2017

Use the conjugate of the denominator to turn it into a whole number. Details below...

#### Explanation:

The first thing you want to do is eliminate the radical expression in the denominator. To do this, multiply top and bottom by the conjugate of the denominator, namely $4 + \sqrt{5}$

$\frac{\left(\sqrt{5} + 2 \sqrt{2}\right) \left(4 + \sqrt{5}\right)}{\left(4 - \sqrt{5}\right) \left(4 + \sqrt{5}\right)}$

Use the FOIL method to multiply top and bottom

$\frac{4 \sqrt{5} + 5 + 8 \sqrt{2} + 2 \sqrt{10}}{16 - 5}$

$\frac{4 \sqrt{5} + 5 + 8 \sqrt{2} + 2 \sqrt{10}}{11}$

I think that is all you can do!