Question

$7.\sqrt{\frac{0.85\times \left(0.105+0.024-0.008\right)}{0.022\times 0.25\times 1.7}}$ simplifies

Answer 1

Dear Student,

$$\begin{gathered} Wehave, \\ \sqrt{\frac{0.85\times 0.105\times 0.024\times 0.008}{0.022\times 0.25\times 1.7}} \\ \sqrt{\frac{{\displaystyle \frac{85}{100}}\times {\displaystyle \frac{105}{1000}}\times {\displaystyle \frac{24}{1000}}\times {\displaystyle \frac{8}{1000}}}{{\displaystyle \frac{22}{1000}}\times {\displaystyle \frac{25}{100}}\times {\displaystyle \frac{17}{10}}}}=\sqrt{\frac{{\displaystyle \frac{85\times 105\times 24\times 8}{100000000000}}}{{\displaystyle \frac{22\times 25\times 17}{1000000}}}} \\ =\sqrt{\frac{85\times 105\times 24\times 8}{22\times 25\times 17}\times \frac{1000000}{100000000000}} \\ =\sqrt{\frac{5\times 17\times 3\times 5\times 7\times 2\times 2\times 2\times 3\times 2\times 2\times 2}{2\times 11\times 5\times 5\times 17}\times \frac{1}{100000}} \\ =\sqrt{\frac{3\times 3\times 2\times 2\times 2\times 2\times 2\times 7}{11\times 100\times 100\times 10}}=\frac{3\times 2\times 2}{100}\sqrt{\frac{2\times 7}{11\times 10}} \\ \frac{3}{25}\sqrt{\frac{7}{55}} \end{gathered}$$

Regards.