# How do you simplify (8+sqrt48)/4?

Apr 12, 2017

$2 + \sqrt{3}$

#### Explanation:

To simplify a square root, use perfect squares such as
${2}^{2} = 4$
${3}^{2} = 9$
${4}^{2} = 16$
$\sqrt{48} = \sqrt{16 \cdot 3}$

Use the rule that says $\sqrt{m \cdot n} = \sqrt{m} \sqrt{n}$

$\sqrt{48} = \sqrt{16} \sqrt{3} = 4 \sqrt{3}$

So $\frac{8 + \sqrt{48}}{4} = \frac{8 + 4 \sqrt{3}}{4}$

Factor a 4 from each number in the numerator:

$\frac{8 + 4 \sqrt{3}}{4} = \frac{4 \left(2 + \sqrt{3}\right)}{4}$

Cancel the 4's because $\frac{4}{4} = 1$

So $\frac{8 + \sqrt{48}}{4} = \frac{8 + 4 \sqrt{3}}{4} = \frac{4 \left(2 + \sqrt{3}\right)}{4} = 2 + \sqrt{3}$