Algebra Examples

$5 \sqrt{- 50} - 3 \sqrt{- 18} + 2 \sqrt{- 8}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $- 50$ as $- 1 (50)$ .

$5 \sqrt{- 1 (50)} - 3 \sqrt{- 18} + 2 \sqrt{- 8}$

Step 1.2

Rewrite $\sqrt{- 1 (50)}$ as $\sqrt{- 1} \cdot \sqrt{50}$ .

$5 (\sqrt{- 1} \cdot \sqrt{50}) - 3 \sqrt{- 18} + 2 \sqrt{- 8}$

Step 1.3

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

$5 (i \cdot \sqrt{50}) - 3 \sqrt{- 18} + 2 \sqrt{- 8}$

Step 1.4

Rewrite $50$ as $5^{2} \cdot 2$ .

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Step 1.4.1

Factor $25$ out of $50$ .

$5 (i \cdot \sqrt{25 (2)}) - 3 \sqrt{- 18} + 2 \sqrt{- 8}$

Step 1.4.2

Rewrite $25$ as $5^{2}$ .

$5 (i \cdot \sqrt{5^{2} \cdot 2}) - 3 \sqrt{- 18} + 2 \sqrt{- 8}$

Step 1.5

Pull terms out from under the radical.

$5 (i \cdot (5 \sqrt{2})) - 3 \sqrt{- 18} + 2 \sqrt{- 8}$

Step 1.6

Move $5$ to the left of $i$ .

$5 (5 \cdot i \sqrt{2}) - 3 \sqrt{- 18} + 2 \sqrt{- 8}$

Step 1.7

Multiply $5$ by $5$ .

$25 (i \sqrt{2}) - 3 \sqrt{- 18} + 2 \sqrt{- 8}$

Step 1.8

Rewrite $- 18$ as $- 1 (18)$ .

$25 i \sqrt{2} - 3 \sqrt{- 1 (18)} + 2 \sqrt{- 8}$

Step 1.9

Rewrite $\sqrt{- 1 (18)}$ as $\sqrt{- 1} \cdot \sqrt{18}$ .

$25 i \sqrt{2} - 3 (\sqrt{- 1} \cdot \sqrt{18}) + 2 \sqrt{- 8}$

Step 1.10

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

$25 i \sqrt{2} - 3 (i \cdot \sqrt{18}) + 2 \sqrt{- 8}$

Step 1.11

Rewrite $18$ as $3^{2} \cdot 2$ .

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Step 1.11.1

Factor $9$ out of $18$ .

$25 i \sqrt{2} - 3 (i \cdot \sqrt{9 (2)}) + 2 \sqrt{- 8}$

Step 1.11.2

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

$25 i \sqrt{2} - 3 (i \cdot \sqrt{3^{2} \cdot 2}) + 2 \sqrt{- 8}$

Step 1.12

Pull terms out from under the radical.

$25 i \sqrt{2} - 3 (i \cdot (3 \sqrt{2})) + 2 \sqrt{- 8}$

Step 1.13

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

$25 i \sqrt{2} - 3 (3 \cdot i \sqrt{2}) + 2 \sqrt{- 8}$

Step 1.14

Multiply $3$ by $- 3$ .

$25 i \sqrt{2} - 9 (i \sqrt{2}) + 2 \sqrt{- 8}$

Step 1.15

Rewrite $- 8$ as $- 1 (8)$ .

$25 i \sqrt{2} - 9 i \sqrt{2} + 2 \sqrt{- 1 (8)}$

Step 1.16

Rewrite $\sqrt{- 1 (8)}$ as $\sqrt{- 1} \cdot \sqrt{8}$ .

$25 i \sqrt{2} - 9 i \sqrt{2} + 2 (\sqrt{- 1} \cdot \sqrt{8})$

Step 1.17

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

$25 i \sqrt{2} - 9 i \sqrt{2} + 2 (i \cdot \sqrt{8})$

Step 1.18

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

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Step 1.18.1

Factor $4$ out of $8$ .

$25 i \sqrt{2} - 9 i \sqrt{2} + 2 (i \cdot \sqrt{4 (2)})$

Step 1.18.2

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

$25 i \sqrt{2} - 9 i \sqrt{2} + 2 (i \cdot \sqrt{2^{2} \cdot 2})$

Step 1.19

Pull terms out from under the radical.

$25 i \sqrt{2} - 9 i \sqrt{2} + 2 (i \cdot (2 \sqrt{2}))$

Step 1.20

Move $2$ to the left of $i$ .

$25 i \sqrt{2} - 9 i \sqrt{2} + 2 (2 \cdot i \sqrt{2})$

Step 1.21

Multiply $2$ by $2$ .

$25 i \sqrt{2} - 9 i \sqrt{2} + 4 i \sqrt{2}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $9 i \sqrt{2}$ from $25 i \sqrt{2}$ .

$16 i \sqrt{2} + 4 i \sqrt{2}$

Step 2.2

Add $16 i \sqrt{2}$ and $4 i \sqrt{2}$ .

$20 i \sqrt{2}$