Question

Simplification of $\frac{3}{\sqrt{8}}+\frac{1}{\sqrt{2}}$ is $\frac{m}{4}\sqrt{2}$, then find the value of $m$.

Answer 1

Given, $\frac{3}{\sqrt{8}}+\frac{1}{\sqrt{2}}=\frac{m}{4}\sqrt{2}$.....................(1)

Now, $\frac{3}{\sqrt{8}}+\frac{1}{\sqrt{2}}$ $=\frac{3}{2\sqrt{2}}+\frac{1}{\sqrt{2}}$
$=\frac{5}{2\sqrt{2}}$ $=\frac{5\times \sqrt{2}}{2\sqrt{2}\times \sqrt{2}}$

$=\frac{5\sqrt{2}}{2\times 2}$ $=\frac{5\sqrt{2}}{4}$.

Then, $\frac{3}{\sqrt{8}}+\frac{1}{\sqrt{2}}$$=\frac{5\sqrt{2}}{4}$....................(2)

Equating equations (1) and (2),

$m=5$