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

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Answer 1 · 2018-05-21T16:51:27

#=(-sqrt3+sqrt3sqrt5)/-4#

#sqrt3/(-1-sqrt5)#

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

#(-1+sqrt5)/(-1+sqrt5) = 1#

#sqrt3/(-1-sqrt5)*(-1+sqrt5)/(-1+sqrt5)#

#=(-sqrt3+sqrt3sqrt5)/(1-sqrt5+sqrt5 - 5)#

#=(-sqrt3+sqrt3sqrt5)/-4#

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