Algebra Examples

$\sqrt{121} - \sqrt{- 81} + \sqrt{144} + \sqrt{- 4}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $121$ as $11^{2}$ .

$\sqrt{11^{2}} - \sqrt{- 81} + \sqrt{144} + \sqrt{- 4}$

Step 1.2

Pull terms out from under the radical.

$| 11 | - \sqrt{- 81} + \sqrt{144} + \sqrt{- 4}$

Step 1.3

The absolute value is the distance between a number and zero. The distance between $0$ and $11$ is $11$ .

$11 - \sqrt{- 81} + \sqrt{144} + \sqrt{- 4}$

Step 1.4

Rewrite $- 81$ as $- 1 (81)$ .

$11 - \sqrt{- 1 (81)} + \sqrt{144} + \sqrt{- 4}$

Step 1.5

Rewrite $\sqrt{- 1 (81)}$ as $\sqrt{- 1} \cdot \sqrt{81}$ .

$11 - (\sqrt{- 1} \cdot \sqrt{81}) + \sqrt{144} + \sqrt{- 4}$

Step 1.6

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

$11 - (i \cdot \sqrt{81}) + \sqrt{144} + \sqrt{- 4}$

Step 1.7

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

$11 - (i \cdot \sqrt{9^{2}}) + \sqrt{144} + \sqrt{- 4}$

Step 1.8

Pull terms out from under the radical.

$11 - (i \cdot | 9 |) + \sqrt{144} + \sqrt{- 4}$

Step 1.9

The absolute value is the distance between a number and zero. The distance between $0$ and $9$ is $9$ .

$11 - (i \cdot 9) + \sqrt{144} + \sqrt{- 4}$

Step 1.10

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

$11 - (9 \cdot i) + \sqrt{144} + \sqrt{- 4}$

Step 1.11

Multiply $9$ by $- 1$ .

$11 - 9 i + \sqrt{144} + \sqrt{- 4}$

Step 1.12

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

$11 - 9 i + \sqrt{12^{2}} + \sqrt{- 4}$

Step 1.13

Pull terms out from under the radical.

$11 - 9 i + | 12 | + \sqrt{- 4}$

Step 1.14

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

$11 - 9 i + 12 + \sqrt{- 4}$

Step 1.15

Rewrite $- 4$ as $- 1 (4)$ .

$11 - 9 i + 12 + \sqrt{- 1 (4)}$

Step 1.16

Rewrite $\sqrt{- 1 (4)}$ as $\sqrt{- 1} \cdot \sqrt{4}$ .

$11 - 9 i + 12 + \sqrt{- 1} \cdot \sqrt{4}$

Step 1.17

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

$11 - 9 i + 12 + i \cdot \sqrt{4}$

Step 1.18

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

$11 - 9 i + 12 + i \cdot \sqrt{2^{2}}$

Step 1.19

Pull terms out from under the radical.

$11 - 9 i + 12 + i \cdot | 2 |$

Step 1.20

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

$11 - 9 i + 12 + i \cdot 2$

Step 1.21

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

$11 - 9 i + 12 + 2 i$

Step 2

Add $11$ and $12$ .

$23 - 9 i + 2 i$

Step 3

Add $- 9 i$ and $2 i$ .

$23 - 7 i$