Algebra Examples

$3 \sqrt{- 12} \cdot 2 \sqrt{- 2}$

Step 1

Rewrite $- 12$ as $- 1 (12)$ .

$3 \sqrt{- 1 (12)} \cdot (2 \sqrt{- 2})$

Step 2

Rewrite $\sqrt{- 1 (12)}$ as $\sqrt{- 1} \cdot \sqrt{12}$ .

$3 (\sqrt{- 1} \cdot \sqrt{12}) \cdot (2 \sqrt{- 2})$

Step 3

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

$3 (i \cdot \sqrt{12}) \cdot (2 \sqrt{- 2})$

Step 4

Rewrite $- 2$ as $- 1 (2)$ .

$3 (i \cdot \sqrt{12}) \cdot (2 \sqrt{- 1 (2)})$

Step 5

Rewrite $\sqrt{- 1 (2)}$ as $\sqrt{- 1} \cdot \sqrt{2}$ .

$3 (i \cdot \sqrt{12}) \cdot (2 (\sqrt{- 1} \cdot \sqrt{2}))$

Step 6

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

$3 (i \cdot \sqrt{12}) \cdot (2 (i \cdot \sqrt{2}))$

Step 7

Rewrite $12$ as $2^{2} \cdot 3$ .

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Step 7.1

Factor $4$ out of $12$ .

$3 (i \cdot \sqrt{4 (3)}) \cdot (2 (i \cdot \sqrt{2}))$

Step 7.2

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

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

Step 8

Pull terms out from under the radical.

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

Step 9

Simplify the expression.

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Step 9.1

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

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

Step 9.2

Multiply $2$ by $3$ .

$6 (i \sqrt{3}) \cdot (2 (i \cdot \sqrt{2}))$

Step 10

Multiply $6 i \sqrt{3} (2 i \sqrt{2})$ .

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Step 10.1

Multiply $2$ by $6$ .

$12 i \sqrt{3} (i \sqrt{2})$

Step 10.2

Raise $i$ to the power of $1$ .

$12 (i^{1} i) \sqrt{3} \sqrt{2}$

Step 10.3

Raise $i$ to the power of $1$ .

$12 (i^{1} i^{1}) \sqrt{3} \sqrt{2}$

Step 10.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$12 i^{1 + 1} \sqrt{3} \sqrt{2}$

Step 10.5

Add $1$ and $1$ .

$12 i^{2} \sqrt{3} \sqrt{2}$

Step 10.6

Combine using the product rule for radicals.

$12 i^{2} \sqrt{2 \cdot 3}$

Step 10.7

Multiply $2$ by $3$ .

$12 i^{2} \sqrt{6}$

Step 11

Rewrite $i^{2}$ as $- 1$ .

$12 \cdot - 1 \sqrt{6}$

Step 12

Multiply $12$ by $- 1$ .

$- 12 \sqrt{6}$

Step 13

The result can be shown in multiple forms.

Exact Form:

$- 12 \sqrt{6}$

Decimal Form:

$- 29.39387691 \dots$