Algebra Examples

$(\sqrt{6}) (4 \sqrt{- 9})$

Step 1

Rewrite $- 9$ as $- 1 (9)$ .

$\sqrt{6} (4 \sqrt{- 1 (9)})$

Step 2

Rewrite $\sqrt{- 1 (9)}$ as $\sqrt{- 1} \cdot \sqrt{9}$ .

$\sqrt{6} (4 (\sqrt{- 1} \cdot \sqrt{9}))$

Step 3

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

$\sqrt{6} (4 (i \cdot \sqrt{9}))$

Step 4

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

$\sqrt{6} (4 (i \cdot \sqrt{3^{2}}))$

Step 5

Pull terms out from under the radical.

$\sqrt{6} (4 (i \cdot | 3 |))$

Step 6

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

$\sqrt{6} (4 (i \cdot 3))$

Step 7

Move $3$ to the left of $i$ .

$\sqrt{6} (4 (3 \cdot i))$

Step 8

Multiply $3$ by $4$ .

$\sqrt{6} (12 i)$

Step 9

Move $12$ to the left of $\sqrt{6}$ .

$12 \sqrt{6} i$