Question

If $\sqrt{0.04\times 0.4\times a}=0.4\times 0.04\times \sqrt{b}$, what is the value of $\frac{a}{b}$?

• A. $0.016$
• B. $1.60$
• C. $0.16$
• D. $16$

Answer 1

Answer: (A)

$0.016$

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

Squaring both the sides :

$\Rightarrow 0.04\times 0.4\times a$ = $(0.4{)}^2\times (0.04{)}^2\times {\sqrt{b}}^2$

$\Rightarrow 0.04\times 0.4\times a$ = $(0.4{)}^2\times (0.04{)}^2\times b$

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

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

$\Rightarrow \frac{a}{b}=0.016$

The value of $\frac{a}{b}$ is $0.016$