Algebra Examples

$- \sqrt{4} + \sqrt{- 200} - \sqrt{1} + \sqrt{- 18}$

Step 1

Simplify each term.

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Step 1.1

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

$- \sqrt{2^{2}} + \sqrt{- 200} - \sqrt{1} + \sqrt{- 18}$

Step 1.2

Pull terms out from under the radical.

$- | 2 | + \sqrt{- 200} - \sqrt{1} + \sqrt{- 18}$

Step 1.3

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$- 1 \cdot 2 + \sqrt{- 200} - \sqrt{1} + \sqrt{- 18}$

Step 1.4

Multiply $- 1$ by $2$ .

$- 2 + \sqrt{- 200} - \sqrt{1} + \sqrt{- 18}$

Step 1.5

Rewrite $- 200$ as $- 1 (200)$ .

$- 2 + \sqrt{- 1 (200)} - \sqrt{1} + \sqrt{- 18}$

Step 1.6

Rewrite $\sqrt{- 1 (200)}$ as $\sqrt{- 1} \cdot \sqrt{200}$ .

$- 2 + \sqrt{- 1} \cdot \sqrt{200} - \sqrt{1} + \sqrt{- 18}$

Step 1.7

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

$- 2 + i \cdot \sqrt{200} - \sqrt{1} + \sqrt{- 18}$

Step 1.8

Rewrite $200$ as $10^{2} \cdot 2$ .

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Step 1.8.1

Factor $100$ out of $200$ .

$- 2 + i \cdot \sqrt{100 (2)} - \sqrt{1} + \sqrt{- 18}$

Step 1.8.2

Rewrite $100$ as $10^{2}$ .

$- 2 + i \cdot \sqrt{10^{2} \cdot 2} - \sqrt{1} + \sqrt{- 18}$

Step 1.9

Pull terms out from under the radical.

$- 2 + i \cdot (| 10 | \sqrt{2}) - \sqrt{1} + \sqrt{- 18}$

Step 1.10

The absolute value is the distance between a number and zero. The distance between $0$ and $10$ is $10$ .

$- 2 + i \cdot (10 \sqrt{2}) - \sqrt{1} + \sqrt{- 18}$

Step 1.11

Move $10$ to the left of $i$ .

$- 2 + 10 \cdot i \sqrt{2} - \sqrt{1} + \sqrt{- 18}$

Step 1.12

Any root of $1$ is $1$ .

$- 2 + 10 i \sqrt{2} - 1 \cdot 1 + \sqrt{- 18}$

Step 1.13

Multiply $- 1$ by $1$ .

$- 2 + 10 i \sqrt{2} - 1 + \sqrt{- 18}$

Step 1.14

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

$- 2 + 10 i \sqrt{2} - 1 + \sqrt{- 1 (18)}$

Step 1.15

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

$- 2 + 10 i \sqrt{2} - 1 + \sqrt{- 1} \cdot \sqrt{18}$

Step 1.16

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

$- 2 + 10 i \sqrt{2} - 1 + i \cdot \sqrt{18}$

Step 1.17

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

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Step 1.17.1

Factor $9$ out of $18$ .

$- 2 + 10 i \sqrt{2} - 1 + i \cdot \sqrt{9 (2)}$

Step 1.17.2

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

$- 2 + 10 i \sqrt{2} - 1 + i \cdot \sqrt{3^{2} \cdot 2}$

Step 1.18

Pull terms out from under the radical.

$- 2 + 10 i \sqrt{2} - 1 + i \cdot (| 3 | \sqrt{2})$

Step 1.19

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

$- 2 + 10 i \sqrt{2} - 1 + i \cdot (3 \sqrt{2})$

Step 1.20

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

$- 2 + 10 i \sqrt{2} - 1 + 3 i \sqrt{2}$

Step 2

Subtract $1$ from $- 2$ .

$10 i \sqrt{2} - 3 + 3 i \sqrt{2}$

Step 3

Add $10 i \sqrt{2}$ and $3 i \sqrt{2}$ .

$13 i \sqrt{2} - 3$

Step 4

Reorder $13 i \sqrt{2}$ and $- 3$ .

$- 3 + 13 i \sqrt{2}$