Algebra Examples

$\sqrt{4} + \sqrt{- 36} - \sqrt{49} + \sqrt{- 49}$

Step 1

Simplify each term.

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Step 1.1

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

$\sqrt{2^{2}} + \sqrt{- 36} - \sqrt{49} + \sqrt{- 49}$

Step 1.2

Pull terms out from under the radical.

$| 2 | + \sqrt{- 36} - \sqrt{49} + \sqrt{- 49}$

Step 1.3

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

$2 + \sqrt{- 36} - \sqrt{49} + \sqrt{- 49}$

Step 1.4

Rewrite $- 36$ as $- 1 (36)$ .

$2 + \sqrt{- 1 (36)} - \sqrt{49} + \sqrt{- 49}$

Step 1.5

Rewrite $\sqrt{- 1 (36)}$ as $\sqrt{- 1} \cdot \sqrt{36}$ .

$2 + \sqrt{- 1} \cdot \sqrt{36} - \sqrt{49} + \sqrt{- 49}$

Step 1.6

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

$2 + i \cdot \sqrt{36} - \sqrt{49} + \sqrt{- 49}$

Step 1.7

Rewrite $36$ as $6^{2}$ .

$2 + i \cdot \sqrt{6^{2}} - \sqrt{49} + \sqrt{- 49}$

Step 1.8

Pull terms out from under the radical.

$2 + i \cdot | 6 | - \sqrt{49} + \sqrt{- 49}$

Step 1.9

The absolute value is the distance between a number and zero. The distance between $0$ and $6$ is $6$ .

$2 + i \cdot 6 - \sqrt{49} + \sqrt{- 49}$

Step 1.10

Move $6$ to the left of $i$ .

$2 + 6 \cdot i - \sqrt{49} + \sqrt{- 49}$

Step 1.11

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

$2 + 6 i - \sqrt{7^{2}} + \sqrt{- 49}$

Step 1.12

Pull terms out from under the radical.

$2 + 6 i - | 7 | + \sqrt{- 49}$

Step 1.13

The absolute value is the distance between a number and zero. The distance between $0$ and $7$ is $7$ .

$2 + 6 i - 1 \cdot 7 + \sqrt{- 49}$

Step 1.14

Multiply $- 1$ by $7$ .

$2 + 6 i - 7 + \sqrt{- 49}$

Step 1.15

Rewrite $- 49$ as $- 1 (49)$ .

$2 + 6 i - 7 + \sqrt{- 1 (49)}$

Step 1.16

Rewrite $\sqrt{- 1 (49)}$ as $\sqrt{- 1} \cdot \sqrt{49}$ .

$2 + 6 i - 7 + \sqrt{- 1} \cdot \sqrt{49}$

Step 1.17

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

$2 + 6 i - 7 + i \cdot \sqrt{49}$

Step 1.18

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

$2 + 6 i - 7 + i \cdot \sqrt{7^{2}}$

Step 1.19

Pull terms out from under the radical.

$2 + 6 i - 7 + i \cdot | 7 |$

Step 1.20

The absolute value is the distance between a number and zero. The distance between $0$ and $7$ is $7$ .

$2 + 6 i - 7 + i \cdot 7$

Step 1.21

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

$2 + 6 i - 7 + 7 i$

Step 2

Subtract $7$ from $2$ .

$- 5 + 6 i + 7 i$

Step 3

Add $6 i$ and $7 i$ .

$- 5 + 13 i$