Question

The value of $(\sqrt{\frac{225}{729}}-\sqrt{\frac{25}{144}})÷\sqrt{\frac{16}{81}}$ is

• A. $\frac{1}{48}$
• B. $\frac{5}{48}$
• C. $\frac{5}{16}$
• D. $\frac{1}{16}$

Answer 1

The correct option is C

$\frac{5}{16}$

$\left[\sqrt{\frac{225}{729}}\right]-\left[\sqrt{\frac{25}{144}}\right]÷\sqrt{\frac{16}{81}}$
$=\{\left[\sqrt{\frac{225}{729}}\right]-\left[\sqrt{\frac{25}{144}}\right]\}÷\frac{4}{9}=[\frac{15}{27}-\frac{5}{12}]÷\frac{4}{9}$
$=[\frac{5}{9}-\frac{5}{12}]÷\frac{4}{9}=\left[\frac{20-15}{36}\right]÷\frac{4}{9}$
$=\frac{5}{36}÷\frac{4}{9}=\frac{5}{36}\times \frac{9}{4}=\frac{5}{16}$