Algebra Examples

$- \sqrt{1} + \sqrt{- 64} - \sqrt{144} + \sqrt{- 9}$

Step 1

Simplify each term.

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Step 1.1

Any root of $1$ is $1$ .

$- 1 \cdot 1 + \sqrt{- 64} - \sqrt{144} + \sqrt{- 9}$

Step 1.2

Multiply $- 1$ by $1$ .

$- 1 + \sqrt{- 64} - \sqrt{144} + \sqrt{- 9}$

Step 1.3

Rewrite $- 64$ as $- 1 (64)$ .

$- 1 + \sqrt{- 1 (64)} - \sqrt{144} + \sqrt{- 9}$

Step 1.4

Rewrite $\sqrt{- 1 (64)}$ as $\sqrt{- 1} \cdot \sqrt{64}$ .

$- 1 + \sqrt{- 1} \cdot \sqrt{64} - \sqrt{144} + \sqrt{- 9}$

Step 1.5

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

$- 1 + i \cdot \sqrt{64} - \sqrt{144} + \sqrt{- 9}$

Step 1.6

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

$- 1 + i \cdot \sqrt{8^{2}} - \sqrt{144} + \sqrt{- 9}$

Step 1.7

Pull terms out from under the radical.

$- 1 + i \cdot | 8 | - \sqrt{144} + \sqrt{- 9}$

Step 1.8

The absolute value is the distance between a number and zero. The distance between $0$ and $8$ is $8$ .

$- 1 + i \cdot 8 - \sqrt{144} + \sqrt{- 9}$

Step 1.9

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

$- 1 + 8 \cdot i - \sqrt{144} + \sqrt{- 9}$

Step 1.10

Rewrite $144$ as $12^{2}$ .

$- 1 + 8 i - \sqrt{12^{2}} + \sqrt{- 9}$

Step 1.11

Pull terms out from under the radical.

$- 1 + 8 i - | 12 | + \sqrt{- 9}$

Step 1.12

The absolute value is the distance between a number and zero. The distance between $0$ and $12$ is $12$ .

$- 1 + 8 i - 1 \cdot 12 + \sqrt{- 9}$

Step 1.13

Multiply $- 1$ by $12$ .

$- 1 + 8 i - 12 + \sqrt{- 9}$

Step 1.14

Rewrite $- 9$ as $- 1 (9)$ .

$- 1 + 8 i - 12 + \sqrt{- 1 (9)}$

Step 1.15

Rewrite $\sqrt{- 1 (9)}$ as $\sqrt{- 1} \cdot \sqrt{9}$ .

$- 1 + 8 i - 12 + \sqrt{- 1} \cdot \sqrt{9}$

Step 1.16

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

$- 1 + 8 i - 12 + i \cdot \sqrt{9}$

Step 1.17

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

$- 1 + 8 i - 12 + i \cdot \sqrt{3^{2}}$

Step 1.18

Pull terms out from under the radical.

$- 1 + 8 i - 12 + i \cdot | 3 |$

Step 1.19

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

$- 1 + 8 i - 12 + i \cdot 3$

Step 1.20

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

$- 1 + 8 i - 12 + 3 i$

Step 2

Subtract $12$ from $- 1$ .

$- 13 + 8 i + 3 i$

Step 3

Add $8 i$ and $3 i$ .

$- 13 + 11 i$