Solve: (√36)/(√2·√3) + (√25)/5 | Adding Fractions with Square Roots

You can only add square roots with the same radicand (number under the radical). Since we have different expressions like $\frac{\sqrt{36}}{\sqrt{6}}$ and $\frac{\sqrt{25}}{5}$, simplify each term separately first.

Use $\frac{a}{\sqrt{b}} = \sqrt{\frac{a^2}{b}}$ when you have a number divided by a square root. For example, $\frac{6}{\sqrt{6}} = \sqrt{\frac{36}{6}} = \sqrt{6}$.

Mathematical expressions can look different but be equal! For instance, $1 + \sqrt{6}$ and $\sqrt{6} + 1$ are the same due to the commutative property of addition.

The product property states that $\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$. So $\sqrt{2} \cdot \sqrt{3} = \sqrt{6}$, which simplifies our denominator.

Yes! Rationalizing $\frac{6}{\sqrt{6}}$ by multiplying top and bottom by $\sqrt{6}$ gives $\frac{6\sqrt{6}}{6} = \sqrt{6}$, the same result!