Question

$\sqrt{\frac{36}{169}} = \square$

Explanation:

Step1: Recall square root property

The square root of a fraction is the fraction of the square roots, i.e., $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ for $a\geq0, b>0$.
So, $\sqrt{\frac{36}{169}}=\frac{\sqrt{36}}{\sqrt{169}}$.

Step2: Calculate square roots

We know that $\sqrt{36} = 6$ (since $6\times6 = 36$) and $\sqrt{169}=13$ (since $13\times13 = 169$).
Then, $\frac{\sqrt{36}}{\sqrt{169}}=\frac{6}{13}$.

Answer:

$\frac{6}{13}$