We have,
\(\sqrt{3{\frac{33}{289}}}\)
= \(\sqrt\frac{900}{289}\)
= \(\frac{\sqrt{900}}{\sqrt{289}}\)
Now, by using long division method we get:
\(\sqrt{289}=17\)
Also,
\(\sqrt{900}=\sqrt{2\times2\times5\times5\times3\times3}\)
= 2 × 5 × 3
= 30
Therefore,
\(\sqrt{3{\frac{33}{289}}}=\frac{30}{17}\)
= \(1\frac{13}{17}\)
