Algebra Examples

$2 \sqrt{- 192} + 5 \sqrt{- 147}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $- 192$ as $- 1 (192)$ .

$2 \sqrt{- 1 (192)} + 5 \sqrt{- 147}$

Step 1.2

Rewrite $\sqrt{- 1 (192)}$ as $\sqrt{- 1} \cdot \sqrt{192}$ .

$2 (\sqrt{- 1} \cdot \sqrt{192}) + 5 \sqrt{- 147}$

Step 1.3

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

$2 (i \cdot \sqrt{192}) + 5 \sqrt{- 147}$

Step 1.4

Rewrite $192$ as $8^{2} \cdot 3$ .

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Step 1.4.1

Factor $64$ out of $192$ .

$2 (i \cdot \sqrt{64 (3)}) + 5 \sqrt{- 147}$

Step 1.4.2

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

$2 (i \cdot \sqrt{8^{2} \cdot 3}) + 5 \sqrt{- 147}$

Step 1.5

Pull terms out from under the radical.

$2 (i \cdot (8 \sqrt{3})) + 5 \sqrt{- 147}$

Step 1.6

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

$2 (8 \cdot i \sqrt{3}) + 5 \sqrt{- 147}$

Step 1.7

Multiply $8$ by $2$ .

$16 (i \sqrt{3}) + 5 \sqrt{- 147}$

Step 1.8

Rewrite $- 147$ as $- 1 (147)$ .

$16 i \sqrt{3} + 5 \sqrt{- 1 (147)}$

Step 1.9

Rewrite $\sqrt{- 1 (147)}$ as $\sqrt{- 1} \cdot \sqrt{147}$ .

$16 i \sqrt{3} + 5 (\sqrt{- 1} \cdot \sqrt{147})$

Step 1.10

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

$16 i \sqrt{3} + 5 (i \cdot \sqrt{147})$

Step 1.11

Rewrite $147$ as $7^{2} \cdot 3$ .

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Step 1.11.1

Factor $49$ out of $147$ .

$16 i \sqrt{3} + 5 (i \cdot \sqrt{49 (3)})$

Step 1.11.2

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

$16 i \sqrt{3} + 5 (i \cdot \sqrt{7^{2} \cdot 3})$

Step 1.12

Pull terms out from under the radical.

$16 i \sqrt{3} + 5 (i \cdot (7 \sqrt{3}))$

Step 1.13

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

$16 i \sqrt{3} + 5 (7 \cdot i \sqrt{3})$

Step 1.14

Multiply $7$ by $5$ .

$16 i \sqrt{3} + 35 i \sqrt{3}$

Step 2

Add $16 i \sqrt{3}$ and $35 i \sqrt{3}$ .

$51 i \sqrt{3}$