# How do you simplify \frac { \sqrt { 63} + 24} { 3}?

Apr 5, 2018

$8 + \sqrt{7}$

#### Explanation:

$\frac{\sqrt{63} + 24}{3}$
=$\frac{\left(\sqrt{9} \times \sqrt{7}\right) + 24}{3}$
=$\frac{\left(3 \times \sqrt{7}\right) + 24}{3}$
=$\frac{3 \left(\sqrt{7} + 8\right)}{3}$
=$8 + \sqrt{7}$

Apr 5, 2018

$\sqrt{7} + 8$
1. First, you would simplify the square root of $63$ by splitting it into $\sqrt{7}$ multiplied by $\sqrt{9}$ (because $9 \times 7 = 63$).
2. Then $\sqrt{9}$ reduces to $3$, so you have $3 \sqrt{7} + 24$ (ignoring the dividing by $3$ for now).
3. Then take $3 \sqrt{7} + 24$ and divide each term by $3$.
4. The $3$'s in $3 \sqrt{7}$ would cancel and give you $\sqrt{7}$.
5. The $24$ divided by $3$ would give you $8$.
6. So your final answer is $\sqrt{7} + 8$