Algebra Examples

$- 21 \sqrt{27 x^{9}}$

Step 1

Rewrite $27 x^{9}$ as ${(3 x^{4})}^{2} \cdot (3 x)$ .

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Step 1.1

Factor $9$ out of $27$ .

$- 21 \sqrt{9 (3) x^{9}}$

Step 1.2

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

$- 21 \sqrt{3^{2} \cdot 3 x^{9}}$

Step 1.3

Factor out $x^{8}$ .

$- 21 \sqrt{3^{2} \cdot 3 (x^{8} x)}$

Step 1.4

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

$- 21 \sqrt{3^{2} \cdot 3 ({(x^{4})}^{2} x)}$

Step 1.5

Move $3$ .

$- 21 \sqrt{3^{2} {(x^{4})}^{2} \cdot 3 x}$

Step 1.6

Rewrite $3^{2} {(x^{4})}^{2}$ as ${(3 x^{4})}^{2}$ .

$- 21 \sqrt{{(3 x^{4})}^{2} \cdot 3 x}$

Step 1.7

Add parentheses.

$- 21 \sqrt{{(3 x^{4})}^{2} \cdot (3 x)}$

Step 2

Pull terms out from under the radical.

$- 21 (3 x^{4} \sqrt{3 x})$

Step 3

Multiply $3$ by $- 21$ .

$- 63 x^{4} \sqrt{3 x}$