Basic Math Examples

$3 \sqrt{- 16} + 2 \sqrt{- 49}$

Step 1

Simplify each term.

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Step 1.1

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

$3 \sqrt{- 1 (16)} + 2 \sqrt{- 49}$

Step 1.2

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

$3 (\sqrt{- 1} \cdot \sqrt{16}) + 2 \sqrt{- 49}$

Step 1.3

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

$3 (i \cdot \sqrt{16}) + 2 \sqrt{- 49}$

Step 1.4

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

$3 (i \cdot \sqrt{4^{2}}) + 2 \sqrt{- 49}$

Step 1.5

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

$3 (i \cdot 4) + 2 \sqrt{- 49}$

Step 1.6

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

$3 (4 \cdot i) + 2 \sqrt{- 49}$

Step 1.7

Multiply $4$ by $3$ .

$12 i + 2 \sqrt{- 49}$

Step 1.8

Rewrite $- 49$ as $- 1 (49)$ .

$12 i + 2 \sqrt{- 1 (49)}$

Step 1.9

Rewrite $\sqrt{- 1 (49)}$ as $\sqrt{- 1} \cdot \sqrt{49}$ .

$12 i + 2 (\sqrt{- 1} \cdot \sqrt{49})$

Step 1.10

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

$12 i + 2 (i \cdot \sqrt{49})$

Step 1.11

Rewrite $49$ as $7^{2}$ .

$12 i + 2 (i \cdot \sqrt{7^{2}})$

Step 1.12

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

$12 i + 2 (i \cdot 7)$

Step 1.13

Move $7$ to the left of $i$ .

$12 i + 2 (7 \cdot i)$

Step 1.14

Multiply $7$ by $2$ .

$12 i + 14 i$

Step 2

Add $12 i$ and $14 i$ .

$26 i$