Finite Math Examples

$3 \sqrt{- 27 x^{6}}$

Step 1

Rewrite $- 27 x^{6}$ as ${(3 x^{3})}^{2} \cdot - 3$ .

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Step 1.1

Factor $9$ out of $- 27$ .

$3 \sqrt{9 (- 3) x^{6}}$

Step 1.2

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

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

Step 1.3

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

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

Step 1.4

Move $- 3$ .

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

Step 1.5

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite $- 3$ as $- 1 (3)$ .

$3 (3 x^{3} \sqrt{- 1 (3)})$

Step 4

Rewrite $\sqrt{- 1 (3)}$ as $\sqrt{- 1} \cdot \sqrt{3}$ .

$3 (3 x^{3} (\sqrt{- 1} \cdot \sqrt{3}))$

Step 5

Rewrite $\sqrt{- 1}$ as $i$ .

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

Step 6

Multiply $3$ by $3$ .

$9 x^{3} i \sqrt{3}$