Simplify: $\frac{1}{\sqrt{2}+\frac{1}{\sqrt{8}}}$
Let's work with the denominator
sqrt 2 + 1 /sqrt 8 =
sqrt 2 + 1 / [2sqrt 2 ] =
[ 2sqrt 2 ] * sqrt 2 + 1
________________ =
2sqrt 2
2 * 2 + 1
_________ =
5 / sqrt 8
So
1 / [ 5 / sqrt 8] =
sqrt 8 2sqrt 2
_____ or _______ (simplified)
5 5
