Originally Posted by

**EvilKitty** Oh, okay!

I got confused with the rule that $\displaystyle (a^2 + b^2)$ can't be factored, and somehow assumed the expression couldn't be factored.

Thanks all, for your help!

P.S. earboth, how did you get $\displaystyle \frac{1}{8} \sqrt{2}$ from $\displaystyle \sqrt{\frac{1}{8}}$? Shouldn't it be $\displaystyle \sqrt{\frac{1}{8}} = \sqrt{2 \times \frac{1}{16}} = \sqrt{\frac{1}{16}}\sqrt{2} = \frac{1}{4}\sqrt{2}$?

Thus $\displaystyle \frac{1}{4} \sqrt{2}+2\sqrt{2}+\frac12\sqrt{2}+\sqrt{2} = \sqrt{2}(\frac{1}{4} + 2 + \frac{1}{2} + 1) = \frac{15}{4}\sqrt{2}$, which is same as Soroban's answer... yay!