Algebra Examples

$\sqrt{- 16} + \sqrt{- 64}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

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

$\sqrt{- 1 (16)} + \sqrt{- 64}$

Step 1.2

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

$\sqrt{- 1} \cdot \sqrt{16} + \sqrt{- 64}$

Step 1.3

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

$i \cdot \sqrt{16} + \sqrt{- 64}$

Step 1.4

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

$i \cdot \sqrt{4^{2}} + \sqrt{- 64}$

Step 1.5

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

$i \cdot 4 + \sqrt{- 64}$

Step 1.6

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

$4 \cdot i + \sqrt{- 64}$

Step 1.7

Rewrite $- 64$ as $- 1 (64)$ .

$4 i + \sqrt{- 1 (64)}$

Step 1.8

Rewrite $\sqrt{- 1 (64)}$ as $\sqrt{- 1} \cdot \sqrt{64}$ .

$4 i + \sqrt{- 1} \cdot \sqrt{64}$

Step 1.9

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

$4 i + i \cdot \sqrt{64}$

Step 1.10

Rewrite $64$ as $8^{2}$ .

$4 i + i \cdot \sqrt{8^{2}}$

Step 1.11

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

$4 i + i \cdot 8$

Step 1.12

Move $8$ to the left of $i$ .

$4 i + 8 i$

Step 2

Add $4 i$ and $8 i$ .

$12 i$