Question

Evaluate: $\sqrt{3\frac{33}{289}}$

Answer 1

$\sqrt{3\frac{33}{289}}=\sqrt{\frac{3\times 289+33}{289}}$
$=\sqrt{\frac{867+33}{289}}=\sqrt{\frac{900}{289}}$

$=\sqrt{\frac{\overline{2\times 2}\times \overline{3\times 3}\times \overline{5\times 5}}{17\times 17}}=\frac{2\times 3\times 5}{17}$
$=\frac{30}{17}=1\frac{13}{17}$