Question

If $\frac{\sqrt{10}-\sqrt{5}}{2\sqrt{2}}$ = $\frac{\sqrt{5}(4-2\sqrt{2})}{m}$.Find $m$

Answer 1

$\frac{\sqrt{10}-\sqrt{5}}{2\sqrt{2}}=\frac{\sqrt{5}(4-2\sqrt{2})}{m}$

$\Rightarrow \frac{\sqrt{10}-\sqrt{5}}{2\sqrt{2}}=\frac{\sqrt{5}\times 2\sqrt{2}(\sqrt{2}-1)}{m}$

$\Rightarrow \frac{\sqrt{10}-\sqrt{5}}{2\sqrt{2}}=\frac{2\sqrt{2}\times (\sqrt{10}-\sqrt{5})}{m}$

$\Rightarrow m=2\sqrt{2}\times 2\sqrt{2}$

$\Rightarrow m=8$