Square roots

$\frac{1}{\sqrt{2}} + \frac{3}{\sqrt{8}}+\frac{5}{\sqrt{32}}$

$= \frac{\sqrt{2}}{\sqrt{2}} \cdot \frac{1}{\sqrt{2}} + \frac{3}{2\sqrt{2}} + \frac{5}{4\sqrt{2}}$

$= \frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{\sqrt{2}} \cdot \frac{3}{2 \sqrt{2}} + \frac{\sqrt{2}}{\sqrt{2}} \cdot \frac{5}{4\sqrt{2}}$

$= \frac{\sqrt{2}}{2} + \frac{3 \sqrt{2}}{4} + \frac{5 \sqrt{2}}{8}$

$= \frac{4 \sqrt{2} + 6\sqrt{2} + 5\sqrt{2}}{8}$

$=\boxed{\frac{15\sqrt{2}}{8}}$

$\frac{1}{\sqrt{2}}+\frac{3}{\sqrt{8}}+\frac{5}{\sqrt{32}}$

$\frac{1}{\sqrt{2}}+\frac{3}{2\sqrt{2}}+\frac{5}{4\sqrt{2}}$

$\frac{4}{4\sqrt{2}}+\frac{6}{4\sqrt{2}}+\frac{5}{4\sqrt{2}}$

$\frac{15}{4\sqrt{2}}$

hmm........ we got different answers

totally forgot alll about that lol

thanks you for reminding me!