trig
posted by lovemath on .
How can I get rid of the square roots in this fraction?
sqrt((2sqrt3))/sqrt((2+sqrt3))
the answer is 2sqrt3
but I don't know how they arrive at it.

Multiply both the numerator and denominator by the conjugate, sqrt((2sqrt3))
Then
sqrt(2sqrt3)/sqrt(2+sqrt3)
=sqrt(2sqrt3)sqrt(2sqrt3)/(sqrt(2+sqrt3)sqrt(2sqrt3))
=sqrt((2sqrt3)²)/sqrt(2²3)
=(2sqrt(3))/sqrt(41)
=(2sqrt(3))/sqrt(1)
=2sqrt(3)