Question

How do you simplify `sqrt2 / (2 sqrt6-sqrt2)`?

Answer 1

The goal is remove roots from denominator. See below

Explanation:

`sqrt2/(2sqrt6-sqrt2)=(sqrt2(2sqrt6+sqrt2))/((2sqrt6-sqrt2)(2sqrt6+sqrt2))=(2sqrt2sqrt6+2)/(24-2)=(2sqrt12+2)/22=sqrt2/11+1/11`