Simplify square root of 162x^2

$\sqrt{162 x^{2}}$

Step 1

Rewrite $162 x^{2}$ as ${(9 x)}^{2} \cdot 2$ .

Factor $81$ out of $162$ .

$\sqrt{81 (2) x^{2}}$

Rewrite $81$ as $9^{2}$ .

$\sqrt{9^{2} \cdot 2 x^{2}}$

Move $2$ .

$\sqrt{9^{2} x^{2} \cdot 2}$

Rewrite $9^{2} x^{2}$ as ${(9 x)}^{2}$ .

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

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

Step 2

Pull terms out from under the radical.

$9 x \sqrt{2}$

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