Question

Can someone point me in the right direction on how to solve this proof?
Note: I'm in PreCalc and these are written as sqr roots not exponents.

(6^1/2 - 2^1/2)/4 = [(2 - 3^1/2)^1/2]/2

Answer 1

let x=(6^1/2-2^1/2)/4
or x=2^1/2(3^1/2-1)/4
Squaring
x^2=2(3+1-2*3^1/2)/16
x^2=(4-2*3^1/2)/8
or x^2=2(2-3^1/2)/8
or x^2=(2-3^1/2)/4
or x={(2-3^1/2)^1/2}/2
=R.H.S