Simplify square root of 6x^2* square root of 18x^2

$\sqrt{6 x^{2}} \cdot \sqrt{18 x^{2}}$

Step 1

Reorder $6$ and $x^{2}$ .

$\sqrt{x^{2} \cdot 6} \cdot \sqrt{18 x^{2}}$

Step 2

Pull terms out from under the radical.

$x \sqrt{6} \cdot \sqrt{18 x^{2}}$

Step 3

Rewrite $18 x^{2}$ as ${(3 x)}^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$x \sqrt{6} \cdot \sqrt{9 (2) x^{2}}$

Rewrite $9$ as $3^{2}$ .

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

Move $2$ .

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

Rewrite $3^{2} x^{2}$ as ${(3 x)}^{2}$ .

$x \sqrt{6} \cdot \sqrt{{(3 x)}^{2} \cdot 2}$

$x \sqrt{6} \cdot \sqrt{{(3 x)}^{2} \cdot 2}$

Step 4

Pull terms out from under the radical.

$x \sqrt{6} \cdot (3 x \sqrt{2})$

Step 5

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$x \cdot x \sqrt{6} \cdot (3 \sqrt{2})$

Multiply $x$ by $x$ .

$x^{2} \sqrt{6} \cdot (3 \sqrt{2})$

$x^{2} \sqrt{6} \cdot (3 \sqrt{2})$

Step 6

Multiply $x^{2} \sqrt{6} (3 \sqrt{2})$ .

Combine using the product rule for radicals.

$x^{2} (3 \sqrt{6 \cdot 2})$

Multiply $6$ by $2$ .

$x^{2} (3 \sqrt{12})$

$x^{2} (3 \sqrt{12})$

Step 7

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

Factor $4$ out of $12$ .

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

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

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

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

Step 8

Pull terms out from under the radical.

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

Step 9

Simplify the expression.

Multiply $2$ by $3$ .

$x^{2} (6 \sqrt{3})$

Move $6$ to the left of $x^{2}$ .

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

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

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