Algebra Examples

$5 \sqrt{- 16} + 3 \sqrt{- 81}$

Step 1

Simplify each term.

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Step 1.1

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

$5 \sqrt{- 1 (16)} + 3 \sqrt{- 81}$

Step 1.2

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

$5 (\sqrt{- 1} \cdot \sqrt{16}) + 3 \sqrt{- 81}$

Step 1.3

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

$5 (i \cdot \sqrt{16}) + 3 \sqrt{- 81}$

Step 1.4

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

$5 (i \cdot \sqrt{4^{2}}) + 3 \sqrt{- 81}$

Step 1.5

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

$5 (i \cdot 4) + 3 \sqrt{- 81}$

Step 1.6

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

$5 (4 \cdot i) + 3 \sqrt{- 81}$

Step 1.7

Multiply $4$ by $5$ .

$20 i + 3 \sqrt{- 81}$

Step 1.8

Rewrite $- 81$ as $- 1 (81)$ .

$20 i + 3 \sqrt{- 1 (81)}$

Step 1.9

Rewrite $\sqrt{- 1 (81)}$ as $\sqrt{- 1} \cdot \sqrt{81}$ .

$20 i + 3 (\sqrt{- 1} \cdot \sqrt{81})$

Step 1.10

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

$20 i + 3 (i \cdot \sqrt{81})$

Step 1.11

Rewrite $81$ as $9^{2}$ .

$20 i + 3 (i \cdot \sqrt{9^{2}})$

Step 1.12

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

$20 i + 3 (i \cdot 9)$

Step 1.13

Move $9$ to the left of $i$ .

$20 i + 3 (9 \cdot i)$

Step 1.14

Multiply $9$ by $3$ .

$20 i + 27 i$

Step 2

Add $20 i$ and $27 i$ .

$47 i$