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

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Answer 1 · 2018-05-24T12:48:14

The goal is remove roots from denominator. See below

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

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