Precalculus Examples

$(\sqrt{- 16}) (\sqrt{- 36})$

Step 1

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

$\sqrt{- 1 (16)} \sqrt{- 36}$

Step 2

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

$\sqrt{- 1} \cdot \sqrt{16} \sqrt{- 36}$

Step 3

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

$i \cdot \sqrt{16} \sqrt{- 36}$

Step 4

Rewrite $- 36$ as $- 1 (36)$ .

$i \cdot \sqrt{16} \sqrt{- 1 (36)}$

Step 5

Rewrite $\sqrt{- 1 (36)}$ as $\sqrt{- 1} \cdot \sqrt{36}$ .

$i \cdot \sqrt{16} (\sqrt{- 1} \cdot \sqrt{36})$

Step 6

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

$i \cdot \sqrt{16} (i \cdot \sqrt{36})$

Step 7

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

$i \cdot \sqrt{4^{2}} (i \cdot \sqrt{36})$

Step 8

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

$i \cdot 4 (i \cdot \sqrt{36})$

Step 9

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

$4 \cdot i (i \cdot \sqrt{36})$

Step 10

Rewrite $36$ as $6^{2}$ .

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

Step 11

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

$4 i (i \cdot 6)$

Step 12

Move $6$ to the left of $i$ .

$4 i (6 \cdot i)$

Step 13

Multiply $4 i (6 i)$ .

Tap for more steps...

Step 13.1

Multiply $6$ by $4$ .

$24 i i$

Step 13.2

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

$24 (i^{1} i)$

Step 13.3

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

$24 (i^{1} i^{1})$

Step 13.4

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

$24 i^{1 + 1}$

Step 13.5

Add $1$ and $1$ .

$24 i^{2}$

Step 14

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

$24 \cdot - 1$

Step 15

Multiply $24$ by $- 1$ .

$- 24$