Evaluate square root of -4* square root of -81

$\sqrt{- 4} \cdot \sqrt{- 81}$

Step 1

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

$\sqrt{- 1 (4)} \cdot \sqrt{- 81}$

Step 2

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

$\sqrt{- 1} \cdot \sqrt{4} \cdot \sqrt{- 81}$

Step 3

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

$i \cdot \sqrt{4} \cdot \sqrt{- 81}$

Step 4

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

$i \cdot \sqrt{4} \cdot \sqrt{- 1 (81)}$

Step 5

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

$i \cdot \sqrt{4} \cdot (\sqrt{- 1} \cdot \sqrt{81})$

Step 6

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

$i \cdot \sqrt{4} \cdot (i \cdot \sqrt{81})$

Step 7

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

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

Step 8

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

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

Step 9

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

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

Step 10

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

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

Step 11

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

$2 i \cdot (i \cdot 9)$

Step 12

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

$2 i \cdot (9 \cdot i)$

Step 13

Multiply $2 i (9 i)$ .

Multiply $9$ by $2$ .

$18 i i$

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

$18 (i^{1} i)$

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

$18 (i^{1} i^{1})$

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

$18 i^{1 + 1}$

Add $1$ and $1$ .

$18 i^{2}$

Step 14

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

$18 \cdot - 1$

Step 15

Multiply $18$ by $- 1$ .

$- 18$

Evaluate square root of -4* square root of -81

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