Question

If $\sqrt{0.4\times 0.4\times a}=0.004\times 0.4\times \sqrt{b},$ then $\frac{a}{b}$ is

• A. $16\times {10}^{-3}$
• B. $16\times {10}^{-4}$
• C. $16\times {10}^{-5}$
• D. $16\times {10}^{-6}$

Answer 1

The correct option is D $16\times {10}^{-6}$

$\sqrt{0.4\times 0.4\times a}=0.004\times 0.4\times \sqrt{b}$

$\Rightarrow \sqrt{0.16\times a}=0.0016\times \sqrt{b}$

$\Rightarrow \sqrt{0.16}\times \sqrt{a}=0.0016\times \sqrt{b}$

$\Rightarrow \frac{\sqrt{a}}{\sqrt{b}}=\frac{0.0016}{\sqrt{0.16}}$

$\Rightarrow \frac{a}{b}=\frac{0.0016\times 0.0016}{0.16}=0.00016$

$\Rightarrow \frac{16}{100000}=16\times {10}^{-6}$