If $$\sqrt {0.04 \times 0.4 \times a} $$ = 0.004 × 0.4 × $$\sqrt b ,$$ then the value of $$\frac{a}{b}\,{\text{is?}}$$ Options: A . &nbsp$${\text{16}} \times {\text{1}}{{\text{0}}^{ - 3}}$$ B . &nbsp$${\text{16}} \times {\text{1}}{{\text{0}}^{ - 4}}$$ C . &nbsp$${\text{16}} \times {\text{1}}{{\text{0}}^{ - 5}}$$ D . &nbsp$${\text{16}} \times {\text{1}}{{\text{0}}^{ - 6}}$$

If $$\sqrt {0.04 \times 0.4 \times a} $$ = 0.004 × 0.4 × $$\sqrt b ,$$

Question

If $$\sqrt {0.04 \times 0.4 \times a} $$ = 0.004 × 0.4 × $$\sqrt b ,$$ then the value of $$\frac{a}{b}\,{\text{is?}}$$

Options:

A . $${\text{16}} \times {\text{1}}{{\text{0}}^{ - 3}}$$

B . $${\text{16}} \times {\text{1}}{{\text{0}}^{ - 4}}$$

C . $${\text{16}} \times {\text{1}}{{\text{0}}^{ - 5}}$$

D . $${\text{16}} \times {\text{1}}{{\text{0}}^{ - 6}}$$

Answer: Option C
$$\eqalign{
& {\text{ }}\sqrt {0.04 \times 0.4 \times a} = 0.004 \times 0.4 \times \sqrt b \cr
& \Rightarrow \sqrt {\frac{4}{{100}} \times \frac{4}{{10}} \times a} = \frac{4}{{1000}} \times \frac{4}{{10}} \times \sqrt b \cr
& \Rightarrow \frac{4}{{10}}\sqrt {\frac{a}{{10}}} = \frac{4}{{10}} \times \frac{4}{{1000}} \times \sqrt b \cr
& \Rightarrow \frac{a}{{10}} = \frac{{16}}{{1000000}} \times b \cr
& \Rightarrow \frac{a}{b} = \frac{{16 \times 10}}{{1000000}} \cr
& \Rightarrow \frac{a}{b} = \frac{{16}}{{100000}} \cr
& \Rightarrow \frac{a}{b} = 16 \times {10^{ - 5}} \cr} $$

Was this answer helpful ?

Next Question