Question

Evaluate $\sqrt{50625}$ and hence find the value of $\sqrt{506.25}+\sqrt{5.0625}$

Answer 1

We have:
$\sqrt{50625}=\sqrt{3\times 3\times 3\times 3\times 5\times 5\times 5\times 5}=3\times 3\times 5\times 5=225$

Next, we will calculate $\sqrt{506.25}\mathrm{and}\sqrt{5.0625}$

$$\begin{gathered} \sqrt{506.25}=\sqrt{\frac{50625}{100}}=\frac{\sqrt{50625}}{\sqrt{100}}=\frac{225}{10}=22.5 \\ \sqrt{5.0625}=\sqrt{\frac{50625}{10000}}=\frac{\sqrt{50625}}{\sqrt{10000}}=\frac{225}{100}=2.25 \\ \sqrt{506.25}+\sqrt{5.0625}=22.5+2.25=24.75 \end{gathered}$$