Solve: Adding Square Roots of Fractions 49/4 and 9/36

The quotient property of square roots says $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$. This works because $\left(\frac{\sqrt{a}}{\sqrt{b}}\right)^2 = \frac{a}{b}$, proving they're equal!

Always reduce the fraction first if possible! For example, $\frac{9}{36} = \frac{1}{4}$, so $\sqrt{\frac{9}{36}} = \sqrt{\frac{1}{4}} = \frac{1}{2}$. This makes calculations much easier.

When denominators are the same, just add the numerators! So $\frac{7}{2} + \frac{1}{2} = \frac{7+1}{2} = \frac{8}{2} = 4$.

Yes, but perfect squares like 4, 9, 16, 25, 36, 49 should be memorized! Knowing $\sqrt{49} = 7$ and $\sqrt{36} = 6$ makes this problem much faster.

In this case, both square roots give you whole numbers (7 and 6), leading to simple fractions. Always check if your final answer can be simplified to a whole number!