Simplify 3x square root of 12+3 square root of 3x^2

$3 x \sqrt{12} + 3 \sqrt{3 x^{2}}$

Step 1

Simplify each term.

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

Factor $4$ out of $12$ .

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

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

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

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

Pull terms out from under the radical.

$3 x (2 \sqrt{3}) + 3 \sqrt{3 x^{2}}$

Multiply $2$ by $3$ .

$6 x \sqrt{3} + 3 \sqrt{3 x^{2}}$

Reorder $3$ and $x^{2}$ .

$6 x \sqrt{3} + 3 \sqrt{x^{2} \cdot 3}$

Pull terms out from under the radical.

$6 x \sqrt{3} + 3 x \sqrt{3}$

$6 x \sqrt{3} + 3 x \sqrt{3}$

Step 2

Add $6 x \sqrt{3}$ and $3 x \sqrt{3}$ .

$9 x \sqrt{3}$

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