Algebra Examples

$\sqrt{100} - \sqrt{- 49} - \sqrt{81} + \sqrt{- 36}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

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

$\sqrt{10^{2}} - \sqrt{- 49} - \sqrt{81} + \sqrt{- 36}$

Step 1.2

Pull terms out from under the radical.

$| 10 | - \sqrt{- 49} - \sqrt{81} + \sqrt{- 36}$

Step 1.3

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

$10 - \sqrt{- 49} - \sqrt{81} + \sqrt{- 36}$

Step 1.4

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

$10 - \sqrt{- 1 (49)} - \sqrt{81} + \sqrt{- 36}$

Step 1.5

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

$10 - (\sqrt{- 1} \cdot \sqrt{49}) - \sqrt{81} + \sqrt{- 36}$

Step 1.6

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

$10 - (i \cdot \sqrt{49}) - \sqrt{81} + \sqrt{- 36}$

Step 1.7

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

$10 - (i \cdot \sqrt{7^{2}}) - \sqrt{81} + \sqrt{- 36}$

Step 1.8

Pull terms out from under the radical.

$10 - (i \cdot | 7 |) - \sqrt{81} + \sqrt{- 36}$

Step 1.9

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

$10 - (i \cdot 7) - \sqrt{81} + \sqrt{- 36}$

Step 1.10

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

$10 - (7 \cdot i) - \sqrt{81} + \sqrt{- 36}$

Step 1.11

Multiply $7$ by $- 1$ .

$10 - 7 i - \sqrt{81} + \sqrt{- 36}$

Step 1.12

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

$10 - 7 i - \sqrt{9^{2}} + \sqrt{- 36}$

Step 1.13

Pull terms out from under the radical.

$10 - 7 i - | 9 | + \sqrt{- 36}$

Step 1.14

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

$10 - 7 i - 1 \cdot 9 + \sqrt{- 36}$

Step 1.15

Multiply $- 1$ by $9$ .

$10 - 7 i - 9 + \sqrt{- 36}$

Step 1.16

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

$10 - 7 i - 9 + \sqrt{- 1 (36)}$

Step 1.17

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

$10 - 7 i - 9 + \sqrt{- 1} \cdot \sqrt{36}$

Step 1.18

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

$10 - 7 i - 9 + i \cdot \sqrt{36}$

Step 1.19

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

$10 - 7 i - 9 + i \cdot \sqrt{6^{2}}$

Step 1.20

Pull terms out from under the radical.

$10 - 7 i - 9 + i \cdot | 6 |$

Step 1.21

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

$10 - 7 i - 9 + i \cdot 6$

Step 1.22

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

$10 - 7 i - 9 + 6 i$

Step 2

Subtract $9$ from $10$ .

$1 - 7 i + 6 i$

Step 3

Add $- 7 i$ and $6 i$ .

$1 - i$