Algebra Examples

$\sqrt{- 12 x^{9}}$

Step 1

Rewrite $- 12 x^{9}$ as ${(2 x^{4})}^{2} \cdot (- 3 x)$ .

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Factor $4$ out of $- 12$ .

$\sqrt{4 (- 3) x^{9}}$

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

$\sqrt{2^{2} \cdot - 3 x^{9}}$

Factor out $x^{8}$ .

$\sqrt{2^{2} \cdot - 3 (x^{8} x)}$

Rewrite $x^{8}$ as ${(x^{4})}^{2}$ .

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

Move $- 3$ .

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

Rewrite $2^{2} {(x^{4})}^{2}$ as ${(2 x^{4})}^{2}$ .

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$2 x^{4} \sqrt{- 3 x}$