Simplify the Radical Expression square root of 12+4 square root of 3

$\sqrt{12} + 4 \sqrt{3}$

Step 1

Simplify each term.

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$\sqrt{4 (3)} + 4 \sqrt{3}$

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} \cdot 3} + 4 \sqrt{3}$

Pull terms out from under the radical.

$| 2 | \sqrt{3} + 4 \sqrt{3}$

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$2 \sqrt{3} + 4 \sqrt{3}$

Step 2

Add $2 \sqrt{3}$ and $4 \sqrt{3}$ .

$6 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt{3}$

Decimal Form:

$10.39230484 \dots$