Simplify 6 square root of 3x^2+x square root of 108

$6 \sqrt{3 x^{2}} + x \sqrt{108}$

Step 1

Simplify each term.

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

$6 \sqrt{x^{2} \cdot 3} + x \sqrt{108}$

Pull terms out from under the radical.

$6 (x \sqrt{3}) + x \sqrt{108}$

Rewrite $108$ as $6^{2} \cdot 3$ .

Factor $36$ out of $108$ .

$6 x \sqrt{3} + x \sqrt{36 (3)}$

Rewrite $36$ as $6^{2}$ .

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

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

Pull terms out from under the radical.

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

Move $6$ to the left of $x$ .

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

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

Step 2

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

$12 x \sqrt{3}$

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