# How do you rationalize the denominator and simplify (8-6sqrt5)/sqrt12?

Mar 1, 2017

$\frac{8 - 6 \sqrt{5}}{\sqrt{12}} = \frac{2 \left(4 - 3 \sqrt{5}\right)}{\sqrt{4 \times 3}}$

$\Rightarrow \frac{2 \left(4 - 3 \sqrt{5}\right)}{2 \sqrt{3}}$

$\Rightarrow \frac{4 - 3 \sqrt{5}}{\sqrt{3}}$ multiply D & N BY$\sqrt{3}$

$\Rightarrow \frac{\sqrt{3} \left(4 - 3 \sqrt{5}\right)}{\sqrt{3} \sqrt{3}}$

$\Rightarrow \frac{\sqrt{3} \left(4 - 3 \sqrt{5}\right)}{3}$