Pre-Algebra Examples

$\sqrt{- 16} - 2 \sqrt{- 4}$

Step 1

Simplify each term.

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Step 1.1

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

$\sqrt{- 1 (16)} - 2 \sqrt{- 4}$

Step 1.2

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

$\sqrt{- 1} \cdot \sqrt{16} - 2 \sqrt{- 4}$

Step 1.3

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

$i \cdot \sqrt{16} - 2 \sqrt{- 4}$

Step 1.4

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

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

Step 1.5

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

$i \cdot 4 - 2 \sqrt{- 4}$

Step 1.6

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

$4 \cdot i - 2 \sqrt{- 4}$

Step 1.7

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

$4 i - 2 \sqrt{- 1 (4)}$

Step 1.8

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

$4 i - 2 (\sqrt{- 1} \cdot \sqrt{4})$

Step 1.9

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

$4 i - 2 (i \cdot \sqrt{4})$

Step 1.10

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

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

Step 1.11

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

$4 i - 2 (i \cdot 2)$

Step 1.12

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

$4 i - 2 (2 \cdot i)$

Step 1.13

Multiply $2$ by $- 2$ .

$4 i - 4 i$

Step 2

Subtract $4 i$ from $4 i$ .

$0$