# How do you simplify sqrt3/(-1-sqrt5)?

May 21, 2018

$= \frac{- \sqrt{3} + \sqrt{3} \sqrt{5}}{-} 4$

#### Explanation:

$\frac{\sqrt{3}}{- 1 - \sqrt{5}}$

you multiply it by the radical conjugate, it doesn't change the value because we are multiplying by 1:

$\frac{- 1 + \sqrt{5}}{- 1 + \sqrt{5}} = 1$

$\frac{\sqrt{3}}{- 1 - \sqrt{5}} \cdot \frac{- 1 + \sqrt{5}}{- 1 + \sqrt{5}}$

$= \frac{- \sqrt{3} + \sqrt{3} \sqrt{5}}{1 - \sqrt{5} + \sqrt{5} - 5}$

$= \frac{- \sqrt{3} + \sqrt{3} \sqrt{5}}{-} 4$

I realize it does not seem simpler but we have removed the radicals from the denominator.