Question

Find the square root by prime factorisation method of 5776

Answer 1

$$\begin{gathered} \mathrm{The}\mathrm{prime}\mathrm{factorisation}\mathrm{of}5776\mathrm{is}: \\ 5776=2\times 2\times 2\times 2\times 19\times 19 \\ \mathrm{So},\sqrt{5776}=\sqrt{\underline{2\times 2}\times \underline{2\times 2}\times \underline{19\times 19}} \\ \Rightarrow \sqrt{5776}=2\times 2\times 19 \\ \Rightarrow \sqrt{5776}=76 \end{gathered}$$