Finite Math Examples

$4 \sqrt{- 64} + 2 \sqrt{- 9}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

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

$4 \sqrt{- 1 (64)} + 2 \sqrt{- 9}$

Step 1.2

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

$4 (\sqrt{- 1} \cdot \sqrt{64}) + 2 \sqrt{- 9}$

Step 1.3

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

$4 (i \cdot \sqrt{64}) + 2 \sqrt{- 9}$

Step 1.4

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

$4 (i \cdot \sqrt{8^{2}}) + 2 \sqrt{- 9}$

Step 1.5

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

$4 (i \cdot 8) + 2 \sqrt{- 9}$

Step 1.6

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

$4 (8 \cdot i) + 2 \sqrt{- 9}$

Step 1.7

Multiply $8$ by $4$ .

$32 i + 2 \sqrt{- 9}$

Step 1.8

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

$32 i + 2 \sqrt{- 1 (9)}$

Step 1.9

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

$32 i + 2 (\sqrt{- 1} \cdot \sqrt{9})$

Step 1.10

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

$32 i + 2 (i \cdot \sqrt{9})$

Step 1.11

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

$32 i + 2 (i \cdot \sqrt{3^{2}})$

Step 1.12

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

$32 i + 2 (i \cdot 3)$

Step 1.13

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

$32 i + 2 (3 \cdot i)$

Step 1.14

Multiply $3$ by $2$ .

$32 i + 6 i$

Step 2

Add $32 i$ and $6 i$ .

$38 i$