Question

If $\sqrt{0.04\times 0.4\times a}=0.4\times 0.04\times \sqrt{b}$ then find the ratio $\frac{a}{b}$.

Answer 1

Given,

$\sqrt{0.04\times 0.4\times a}=0.4\times 0.04\times \sqrt{b}$

$\Rightarrow \frac{\sqrt{a}}{\sqrt{b}}=\frac{0.4\times 0.04}{\sqrt{0.04\times 0.4}}$

$\Rightarrow \frac{\sqrt{a}}{\sqrt{b}}=\sqrt{0.4\times 0.04}$

squaring on both sides, we get,

$\Rightarrow \frac{a}{b}=0.4\times 0.04=0.016$