Evaluate:

$\sqrt{3 \frac{13}{36}}$

$=\sqrt{\frac{121}{36}}$

$=\frac{\sqrt{121}}{\sqrt{36}}$

$=\frac{\sqrt{11 \times 11}}{\sqrt{6 \times 6}}$

$=\frac{11}{6}$

$=1 \frac{5}{11}$