Evaluate:

$\sqrt{3 \frac{33}{289}}=\sqrt{\frac{900}{289}}=\frac{\sqrt{900}}{\sqrt{289}}$

Using long division method:

$\sqrt{289}=17$

And

$\sqrt{900}=\sqrt{2 \times 2 \times 5 \times 5 \times 3 \times 3}=2 \times 5 \times 3=30$

$\therefore \sqrt{3 \frac{33}{289}}=\frac{30}{17}=1 \frac{13}{17}$