Question

How can I get rid of the square roots in this fraction?

sqrt((2-sqrt3))/sqrt((2+sqrt3))

the answer is 2-sqrt3

but I don't know how they arrive at it.

Answer 1

Multiply both the numerator and denominator by the conjugate, sqrt((2-sqrt3))

Then
sqrt(2-sqrt3)/sqrt(2+sqrt3)
=sqrt(2-sqrt3)sqrt(2-sqrt3)/(sqrt(2+sqrt3)sqrt(2-sqrt3))
=sqrt((2-sqrt3)²)/sqrt(2²-3)
=(2-sqrt(3))/sqrt(4-1)
=(2-sqrt(3))/sqrt(1)
=2-sqrt(3)