Write in the form , where and are positive integers:
\[\frac{1}{\sqrt{2}} +\frac{3}{\sqrt{8}} + \frac{6}{\sqrt{32}}.\]
Multiplying each term by sqrt(2) / sqrt(2)
1/sqrt(2) + 3/sqrt(8) + 6/sqrt(32)
= sqrt(2) / sqrt(4) + 3sqrt(2) / sqrt(16) + 6sqrt(2)/sqrt(64)
= sqrt(2) / 2 + 3sqrt(2) / 4 + 6sqrt(2) / 8
= 2sqrt(2) / 4 + 3sqrt(2) / 4 + 3sqrt(2) / 4 (writing each fraction with a denominator of 4)
= 8sqrt(2) / 4
= 2sqrt(2)