Algebra Examples

$\sqrt{- 4} \cdot \sqrt{27}$

Step 1

Rewrite $- 4$ as $- 1 (4)$ .

$\sqrt{- 1 (4)} \cdot \sqrt{27}$

Step 2

Rewrite $\sqrt{- 1 (4)}$ as $\sqrt{- 1} \cdot \sqrt{4}$ .

$\sqrt{- 1} \cdot \sqrt{4} \cdot \sqrt{27}$

Step 3

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

$i \cdot \sqrt{4} \cdot \sqrt{27}$

Step 4

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

$i \cdot \sqrt{2^{2}} \cdot \sqrt{27}$

Step 5

Pull terms out from under the radical, assuming positive real numbers.

$i \cdot 2 \cdot \sqrt{27}$

Step 6

Move $2$ to the left of $i$ .

$2 \cdot i \cdot \sqrt{27}$

Step 7

Rewrite $27$ as $3^{2} \cdot 3$ .

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Step 7.1

Factor $9$ out of $27$ .

$2 i \cdot \sqrt{9 (3)}$

Step 7.2

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

$2 i \cdot \sqrt{3^{2} \cdot 3}$

Step 8

Pull terms out from under the radical.

$2 i \cdot (3 \sqrt{3})$

Step 9

Multiply $3$ by $2$ .

$6 i \sqrt{3}$