Question

Find the sub-triplicate ratio of the following:

iii) $125a^3:343b^6$

Answer 1

Given:$125a^3:343b^6$

$125a^3:343b^6=\frac{125a^3}{343b^6}=\frac{5^3{a}^3}{7^3{b}^6}$

So, the sub-triplicate ratio of $125a^3:343b^6$ is,

$\sqrt[3]{3\frac{125a^3}{343b^6}}$

$=\sqrt[3]{3\frac{(5a{)}^3}{(7b^2{)}^3}}$

$={\left(\frac{(5a{)}^3}{(7b^2{)}^3}\right)}^{\frac{1}{3}}$

$=\frac{5a}{7b^2}$

Hence, the sub-triplicate ratio of $125a^3:343b^6\text{is}5a:7b^2$