How do you simplify $\frac{\sqrt{3}}{- 1 - \sqrt{5}}$ $sqrt3/(-1-sqrt5)$ ?

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Answer 1 · 2018-05-21T16:51:27

$= \frac{- \sqrt{3} + \sqrt{3} \sqrt{5}}{- 4}$ $=(-sqrt3+sqrt3sqrt5)/-4$

$\frac{\sqrt{3}}{- 1 - \sqrt{5}}$ $sqrt3/(-1-sqrt5)$

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

$\frac{- 1 + \sqrt{5}}{- 1 + \sqrt{5}} = 1$ $(-1+sqrt5)/(-1+sqrt5) = 1$

$\frac{\sqrt{3}}{- 1 - \sqrt{5}} \cdot \frac{- 1 + \sqrt{5}}{- 1 + \sqrt{5}}$ $sqrt3/(-1-sqrt5)*(-1+sqrt5)/(-1+sqrt5)$

$= \frac{- \sqrt{3} + \sqrt{3} \sqrt{5}}{1 - \sqrt{5} + \sqrt{5} - 5}$ $=(-sqrt3+sqrt3sqrt5)/(1-sqrt5+sqrt5 - 5)$

$= \frac{- \sqrt{3} + \sqrt{3} \sqrt{5}}{- 4}$ $=(-sqrt3+sqrt3sqrt5)/-4$

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

How do you simplify sqrt3/(-1-sqrt5)√3−1−√5sqrt3/(-1-sqrt5)?