Algebra Examples

$\sqrt{- 162} + 2 \sqrt{- 32} - 3 \sqrt{- 98}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $- 162$ as $- 1 (162)$ .

$\sqrt{- 1 (162)} + 2 \sqrt{- 32} - 3 \sqrt{- 98}$

Step 1.2

Rewrite $\sqrt{- 1 (162)}$ as $\sqrt{- 1} \cdot \sqrt{162}$ .

$\sqrt{- 1} \cdot \sqrt{162} + 2 \sqrt{- 32} - 3 \sqrt{- 98}$

Step 1.3

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

$i \cdot \sqrt{162} + 2 \sqrt{- 32} - 3 \sqrt{- 98}$

Step 1.4

Rewrite $162$ as $9^{2} \cdot 2$ .

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Step 1.4.1

Factor $81$ out of $162$ .

$i \cdot \sqrt{81 (2)} + 2 \sqrt{- 32} - 3 \sqrt{- 98}$

Step 1.4.2

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

$i \cdot \sqrt{9^{2} \cdot 2} + 2 \sqrt{- 32} - 3 \sqrt{- 98}$

Step 1.5

Pull terms out from under the radical.

$i \cdot (9 \sqrt{2}) + 2 \sqrt{- 32} - 3 \sqrt{- 98}$

Step 1.6

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

$9 \cdot i \sqrt{2} + 2 \sqrt{- 32} - 3 \sqrt{- 98}$

Step 1.7

Rewrite $- 32$ as $- 1 (32)$ .

$9 i \sqrt{2} + 2 \sqrt{- 1 (32)} - 3 \sqrt{- 98}$

Step 1.8

Rewrite $\sqrt{- 1 (32)}$ as $\sqrt{- 1} \cdot \sqrt{32}$ .

$9 i \sqrt{2} + 2 (\sqrt{- 1} \cdot \sqrt{32}) - 3 \sqrt{- 98}$

Step 1.9

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

$9 i \sqrt{2} + 2 (i \cdot \sqrt{32}) - 3 \sqrt{- 98}$

Step 1.10

Rewrite $32$ as $4^{2} \cdot 2$ .

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Step 1.10.1

Factor $16$ out of $32$ .

$9 i \sqrt{2} + 2 (i \cdot \sqrt{16 (2)}) - 3 \sqrt{- 98}$

Step 1.10.2

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

$9 i \sqrt{2} + 2 (i \cdot \sqrt{4^{2} \cdot 2}) - 3 \sqrt{- 98}$

Step 1.11

Pull terms out from under the radical.

$9 i \sqrt{2} + 2 (i \cdot (4 \sqrt{2})) - 3 \sqrt{- 98}$

Step 1.12

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

$9 i \sqrt{2} + 2 (4 \cdot i \sqrt{2}) - 3 \sqrt{- 98}$

Step 1.13

Multiply $4$ by $2$ .

$9 i \sqrt{2} + 8 (i \sqrt{2}) - 3 \sqrt{- 98}$

Step 1.14

Rewrite $- 98$ as $- 1 (98)$ .

$9 i \sqrt{2} + 8 i \sqrt{2} - 3 \sqrt{- 1 (98)}$

Step 1.15

Rewrite $\sqrt{- 1 (98)}$ as $\sqrt{- 1} \cdot \sqrt{98}$ .

$9 i \sqrt{2} + 8 i \sqrt{2} - 3 (\sqrt{- 1} \cdot \sqrt{98})$

Step 1.16

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

$9 i \sqrt{2} + 8 i \sqrt{2} - 3 (i \cdot \sqrt{98})$

Step 1.17

Rewrite $98$ as $7^{2} \cdot 2$ .

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Step 1.17.1

Factor $49$ out of $98$ .

$9 i \sqrt{2} + 8 i \sqrt{2} - 3 (i \cdot \sqrt{49 (2)})$

Step 1.17.2

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

$9 i \sqrt{2} + 8 i \sqrt{2} - 3 (i \cdot \sqrt{7^{2} \cdot 2})$

Step 1.18

Pull terms out from under the radical.

$9 i \sqrt{2} + 8 i \sqrt{2} - 3 (i \cdot (7 \sqrt{2}))$

Step 1.19

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

$9 i \sqrt{2} + 8 i \sqrt{2} - 3 (7 \cdot i \sqrt{2})$

Step 1.20

Multiply $7$ by $- 3$ .

$9 i \sqrt{2} + 8 i \sqrt{2} - 21 i \sqrt{2}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $9 i \sqrt{2}$ and $8 i \sqrt{2}$ .

$17 i \sqrt{2} - 21 i \sqrt{2}$

Step 2.2

Subtract $21 i \sqrt{2}$ from $17 i \sqrt{2}$ .

$- 4 i \sqrt{2}$