Algebra Examples

$\sqrt{100} + \sqrt{- 1} + \sqrt{1} - \sqrt{- 25}$

Step 1

Simplify each term.

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Step 1.1

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

$\sqrt{10^{2}} + \sqrt{- 1} + \sqrt{1} - \sqrt{- 25}$

Step 1.2

Pull terms out from under the radical.

$| 10 | + \sqrt{- 1} + \sqrt{1} - \sqrt{- 25}$

Step 1.3

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

$10 + \sqrt{- 1} + \sqrt{1} - \sqrt{- 25}$

Step 1.4

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

$10 + i + \sqrt{1} - \sqrt{- 25}$

Step 1.5

Any root of $1$ is $1$ .

$10 + i + 1 - \sqrt{- 25}$

Step 1.6

Rewrite $- 25$ as $- 1 (25)$ .

$10 + i + 1 - \sqrt{- 1 (25)}$

Step 1.7

Rewrite $\sqrt{- 1 (25)}$ as $\sqrt{- 1} \cdot \sqrt{25}$ .

$10 + i + 1 - (\sqrt{- 1} \cdot \sqrt{25})$

Step 1.8

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

$10 + i + 1 - (i \cdot \sqrt{25})$

Step 1.9

Rewrite $25$ as $5^{2}$ .

$10 + i + 1 - (i \cdot \sqrt{5^{2}})$

Step 1.10

Pull terms out from under the radical.

$10 + i + 1 - (i \cdot | 5 |)$

Step 1.11

The absolute value is the distance between a number and zero. The distance between $0$ and $5$ is $5$ .

$10 + i + 1 - (i \cdot 5)$

Step 1.12

Move $5$ to the left of $i$ .

$10 + i + 1 - (5 \cdot i)$

Step 1.13

Multiply $5$ by $- 1$ .

$10 + i + 1 - 5 i$

Step 2

Add $10$ and $1$ .

$11 + i - 5 i$

Step 3

Subtract $5 i$ from $i$ .

$11 - 4 i$