Algebra Examples

$(6 \sqrt{- 4}) (\sqrt{- 1})$

Step 1

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

$6 \sqrt{- 1 (4)} \sqrt{- 1}$

Step 2

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

$6 (\sqrt{- 1} \cdot \sqrt{4}) \sqrt{- 1}$

Step 3

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

$6 (i \cdot \sqrt{4}) \sqrt{- 1}$

Step 4

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

$6 (i \cdot \sqrt{4}) i$

Step 5

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

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

Step 6

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

$6 (i \cdot 2) i$

Step 7

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

$6 (2 \cdot i) i$

Step 8

Multiply $2$ by $6$ .

$12 i i$

Step 9

Multiply $12 i i$ .

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Step 9.1

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

$12 (i^{1} i)$

Step 9.2

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

$12 (i^{1} i^{1})$

Step 9.3

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

$12 i^{1 + 1}$

Step 9.4

Add $1$ and $1$ .

$12 i^{2}$

Step 10

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

$12 \cdot - 1$

Step 11

Multiply $12$ by $- 1$ .

$- 12$