Evaluate:

$\sqrt{4 \frac{73}{324}}=\sqrt{\frac{1369}{324}}=\frac{\sqrt{1369}}{\sqrt{324}}$

Using long division method:

$\sqrt{1369}=37$

$\sqrt{324}=\sqrt{2 \times 2 \times 9 \times 9}=2 \times 9=18$

$\therefore \sqrt{4 \frac{73}{324}}=\frac{37}{18}=2 \frac{1}{18}$