Question:
Evaluate $\sqrt{50625}$ and hence find the value of $\sqrt{506.25}+\sqrt{5.0625}$
Solution:
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 $\sqrt{506.25}$ and $\sqrt{5.0625}$
$\sqrt{506.25}=\sqrt{\frac{50625}{100}}=\frac{\sqrt{50625}}{\sqrt{100}}=\frac{225}{10}=22.5$
$\sqrt{5.0625}=\sqrt{\frac{50625}{10000}}=\frac{\sqrt{50625}}{\sqrt{10000}}=\frac{225}{100}=2.25$
$\sqrt{506.25}+\sqrt{5.0625}=22.5+2.25=24.75$
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