Question

FIND THE SQUARE ROOT OF 2304 AND 1764 AND FIND THE SQUARE ROOT OF 0.2304 + 0.1764

Answer 1

$$\begin{gathered} \mathrm{The}\mathrm{prime}\mathrm{factorisation}\mathrm{of}2304\mathrm{is}: \\ 2304=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 3\times 3 \\ \Rightarrow \sqrt{2304}=\sqrt{2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 3\times 3}=2\times 2\times 2\times 2\times 3=48 \\ \mathrm{The}\mathrm{prime}\mathrm{factorisation}\mathrm{of}1764\mathrm{is}: \\ 1764=2\times 2\times 3\times 3\times 7\times 7 \\ \Rightarrow \sqrt{1764}=\sqrt{2\times 2\times 3\times 3\times 7\times 7}=2\times 3\times 7=42 \\ \mathrm{Now},\sqrt{0.2304}+\sqrt{0.1764}=\sqrt{\frac{2304}{10000}}+\sqrt{\frac{1764}{10000}}=\frac{48}{100}+\frac{42}{100}=0.48+0.42=1.00 \end{gathered}$$