Question

Find the triplicate ratio of the following:
iii)$\sqrt{15}:\sqrt{18}$

Answer 1

Given:$\sqrt{15}:\sqrt{18}=\frac{\sqrt{15}}{\sqrt{18}}$

$\frac{\sqrt{15}}{\sqrt{18}}=\frac{\sqrt{15}}{\sqrt{3\times 3\times 2}}=\frac{\sqrt{15}}{3\sqrt{2}}$

So, the triplicate ratio of $\sqrt{15}:\sqrt{18}$ is,

${\left(\frac{\sqrt{15}}{\sqrt{18}}\right)}^3={\left(\frac{\sqrt{15}}{3\sqrt{2}}\right)}^3$

$=\frac{15\sqrt{15}}{27\times 2\sqrt{2}}=\frac{5\sqrt{15}}{9\times 2\sqrt{2}}=\frac{5\sqrt{15}}{18\sqrt{2}}$

Hence, the triplicate ratio of $\sqrt{15}:\sqrt{18}\text{is}5\sqrt{15}:18\sqrt{2}$.