Evaluate square root of -9* square root of -16

$\sqrt{- 9} \cdot \sqrt{- 16}$

Step 1

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

$\sqrt{- 1 (9)} \cdot \sqrt{- 16}$

Step 2

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

$\sqrt{- 1} \cdot \sqrt{9} \cdot \sqrt{- 16}$

Step 3

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

$i \cdot \sqrt{9} \cdot \sqrt{- 16}$

Step 4

Rewrite $- 16$ as $- 1 (16)$ .

$i \cdot \sqrt{9} \cdot \sqrt{- 1 (16)}$

Step 5

Rewrite $\sqrt{- 1 (16)}$ as $\sqrt{- 1} \cdot \sqrt{16}$ .

$i \cdot \sqrt{9} \cdot (\sqrt{- 1} \cdot \sqrt{16})$

Step 6

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

$i \cdot \sqrt{9} \cdot (i \cdot \sqrt{16})$

Step 7

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

$i \cdot \sqrt{3^{2}} \cdot (i \cdot \sqrt{16})$

Step 8

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

$i \cdot 3 \cdot (i \cdot \sqrt{16})$

Step 9

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

$3 \cdot i \cdot (i \cdot \sqrt{16})$

Step 10

Rewrite $16$ as $4^{2}$ .

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

Step 11

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

$3 i \cdot (i \cdot 4)$

Step 12

Move $4$ to the left of $i$ .

$3 i \cdot (4 \cdot i)$

Step 13

Multiply $3 i (4 i)$ .

Multiply $4$ by $3$ .

$12 i i$

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

$12 (i^{1} i)$

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

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

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

$12 i^{1 + 1}$

Add $1$ and $1$ .

$12 i^{2}$

Step 14

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

$12 \cdot - 1$

Step 15

Multiply $12$ by $- 1$ .

$- 12$

Evaluate square root of -9* square root of -16

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