Question

Show that

$\frac{16}{\sqrt{50}\sqrt{6}}=\frac{16}{5\sqrt{2}\sqrt{6}}=\frac{8\sqrt{3}}{15}$

Answer 1

$\frac{16}{\sqrt{50}\sqrt{6}}=\frac{16}{5\sqrt{2}\sqrt{6}}$

$\to \frac{1}{\sqrt{50}}=\frac{1}{5\sqrt{2}}$

$\to \frac{1}{\sqrt{50}}=\frac{1}{\sqrt{25\times 2}}$

$\to \frac{1}{\sqrt{50}}=\frac{1}{\sqrt{50}}$...(1)

$\frac{16}{5\sqrt{2}\sqrt{6}}=\frac{8\sqrt{3}}{15}$

$\to \frac{2}{\sqrt{2}\sqrt{6}}=\frac{\sqrt{3}}{3}$

$\to \frac{\sqrt{2}}{\sqrt{6}}=\frac{1}{\sqrt{3}}$

$\to \frac{\sqrt{2}}{\sqrt{2}}=1$

$\to 1=1$...(2)

From (1) and (2)

It's clear that

$\frac{16}{\sqrt{50}\sqrt{6}}=\frac{16}{5\sqrt{2}\sqrt{6}}=\frac{8\sqrt{3}}{15}$