Algebra Examples

$\sqrt{- 81} \cdot {(- 2 i)}^{2}$

Step 1

Rewrite $- 81$ as $- 1 (81)$ .

$\sqrt{- 1 (81)} \cdot {(- 2 i)}^{2}$

Step 2

Rewrite $\sqrt{- 1 (81)}$ as $\sqrt{- 1} \cdot \sqrt{81}$ .

$\sqrt{- 1} \cdot \sqrt{81} \cdot {(- 2 i)}^{2}$

Step 3

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

$i \cdot \sqrt{81} \cdot {(- 2 i)}^{2}$

Step 4

Rewrite $81$ as $9^{2}$ .

$i \cdot \sqrt{9^{2}} \cdot {(- 2 i)}^{2}$

Step 5

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

$i \cdot 9 \cdot {(- 2 i)}^{2}$

Step 6

Move $9$ to the left of $i$ .

$9 \cdot i \cdot {(- 2 i)}^{2}$

Step 7

Apply the product rule to $- 2 i$ .

$9 i \cdot ({(- 2)}^{2} i^{2})$

Step 8

Raise $- 2$ to the power of $2$ .

$9 i \cdot (4 i^{2})$

Step 9

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

$9 i \cdot (4 \cdot - 1)$

Step 10

Multiply $4$ by $- 1$ .

$9 i \cdot - 4$

Step 11

Multiply $- 4$ by $9$ .

$- 36 i$