# How do you simplify 14 /(sqrt5 + sqrt3)?

Jan 31, 2016

This is completely simplified if you want to combine radicals. However, we can simplify further by rationalizing the denomiator.

#### Explanation:

To rationalize the denomiator, we must multiply the entire expression by the conjugate of the denominator. The conjugate forms a difference of squares with the denominator so to cancel out the radicals.

$\frac{14}{\sqrt{5} + \sqrt{3}}$

The conjugate would be $\sqrt{5} - \sqrt{3}$

$\frac{14}{\sqrt{5} + \sqrt{3}} \times \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} - \sqrt{3}}$

$\frac{14 \sqrt{5} - 14 \sqrt{3}}{\sqrt{25} + \sqrt{15} - \sqrt{15} - \sqrt{9}}$

$\frac{14 \sqrt{5} - 14 \sqrt{3}}{5 - 3}$

$\frac{14 \sqrt{5} - 14 \sqrt{3}}{2}$

$7 \sqrt{5} - 7 \sqrt{3}$

The answer is $7 \sqrt{5} - 7 \sqrt{3}$.

Hopefully this helps!