Question

√0.04×√0.4×√a=0.4×0.04×√b then find the ratio a/b

Answer 1

$\sqrt{0.04} \times \sqrt{0.4} \times \sqrt{a} = 0.4 \times 0.04 \times \sqrt{b} \\ \sqrt{ \frac{4}{100} } \times \sqrt{ \frac{4}{10} } \times \sqrt{a} = \frac{4}{10} \times \frac{4}{100} \times \sqrt{b} \\ \frac{2}{10} \times \frac{2}{ \sqrt{10} } \times \sqrt{a} = \frac{16}{1000} \times \sqrt{b} \\ \frac{2}{5} \times \frac{a}{10} = \frac{2}{125} \times \sqrt{b} \\ \frac{a}{25} = \frac{2 \sqrt{b} }{125} \\ a \: = \frac{2 \sqrt{b} }{125} \times 25 \\ a = \frac{2 \sqrt{b} }{5} \\ 5a \: = 2 \sqrt{b } \\ 2.5a = \sqrt{b} \\ {6.25a}^{2} = b$

6.25 a^2 : b