Find the \sqrt{ (100)/(144) } as a fraction

Question

Find the

`\sqrt{ (100)/(144) }`
as a fraction

Answer 1

`\bf \sqrt{\cfrac{100}{144}}~~ \begin{cases} 100=10\cdot 10\\ \qquad 10^2\\ 144=12\cdot 12\\ \qquad 12^2 \end{cases}\implies \sqrt{\cfrac{10^2}{12^2}}\implies \cfrac{10}{12}\implies \stackrel{simplified}{\cfrac{5}{6}}`