Question

Find the value of $x$ in the equation given below.
$(\sqrt{\frac{121}{144}}+\sqrt{\frac{9}{16}})\sqrt{\frac{x}{100}}=\frac{8}{3}$

Answer 1

$(\sqrt{\frac{121}{144}}+\sqrt{\frac{9}{16}})=\sqrt{\frac{x}{100}}=\frac{8}{3}$

$(\frac{11}{12}+\frac{3}{4})\left(\frac{\sqrt{x}}{10}\right)=\frac{8}{3}$

$\left(\frac{11+9}{12}\right)\frac{\sqrt{x}}{10}=\frac{8}{3}$

$\frac{20}{12}\times \frac{\sqrt{x}}{10}=\frac{8}{3}$

$\sqrt{x}=\frac{8}{3}\times \frac{10}{2}=16$

$\therefore x=16\times 16=256$