Evaluate 4 square root of 3+2 square root of 12

$4 \sqrt{3} + 2 \sqrt{12}$

Step 1

Simplify each term.

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

Factor $4$ out of $12$ .

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

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

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

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

Pull terms out from under the radical.

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

Multiply $2$ by $2$ .

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

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

Step 2

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

$8 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$8 \sqrt{3}$

Decimal Form:

$13.85640646 \dots$

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