Question

Find the sub-duplicate ratio of the following:
ii) $63m^2:28n^2$

Answer 1

Given: $63m^2:28n^2$

$63m^2:28n^2=\frac{63m^2}{28n^2}=\frac{9\times 7m^2}{4\times 7n^2}=\frac{9m^2}{4n^2}$

So, the sub-duplicate ratio of $63m^2:28n^2$ is,

$\sqrt{\frac{63m^2}{28n^2}}$

$=\sqrt{\frac{9m^2}{4n^2}}$

$={\left(\frac{9m^2}{4n^2}\right)}^{\frac{1}{2}}$

$={\left(\frac{3^2{m}^2}{2^2{n}^2}\right)}^{\frac{1}{2}}$

$=\frac{3m}{2n}$

Hence, the sub-duplicate ratio of $63m^2:28n^2\text{is}3m:2n$.