# Evaluate: /(sqrt() 3+\sqrt{) 2} sqrt() 6

## Expression: $$\frac { \sqrt { 3 } + \sqrt { 2 } } { \sqrt { 6 } }$$

Rationalize the denominator of $\frac{\sqrt{3}+\sqrt{2}}{\sqrt{6}}$ by multiplying numerator and denominator by $\sqrt{6}$.

$$\frac{\left(\sqrt{3}+\sqrt{2}\right)\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of $\sqrt{6}$ is $6$.

$$\frac{\left(\sqrt{3}+\sqrt{2}\right)\sqrt{6}}{6}$$

Use the distributive property to multiply $\sqrt{3}+\sqrt{2}$ by $\sqrt{6}$.

$$\frac{\sqrt{3}\sqrt{6}+\sqrt{2}\sqrt{6}}{6}$$

Factor $6=3\times 2$. Rewrite the square root of the product $\sqrt{3\times 2}$ as the product of square roots $\sqrt{3}\sqrt{2}$.

$$\frac{\sqrt{3}\sqrt{3}\sqrt{2}+\sqrt{2}\sqrt{6}}{6}$$

Multiply $\sqrt{3}$ and $\sqrt{3}$ to get $3$.

$$\frac{3\sqrt{2}+\sqrt{2}\sqrt{6}}{6}$$

Factor $6=2\times 3$. Rewrite the square root of the product $\sqrt{2\times 3}$ as the product of square roots $\sqrt{2}\sqrt{3}$.

$$\frac{3\sqrt{2}+\sqrt{2}\sqrt{2}\sqrt{3}}{6}$$

Multiply $\sqrt{2}$ and $\sqrt{2}$ to get $2$.

$$\frac{3\sqrt{2}+2\sqrt{3}}{6}$$

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