Algebra Examples

$- \sqrt{1} - \sqrt{- 100} - \sqrt{121} + \sqrt{- 1}$

Step 1

Simplify each term.

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Step 1.1

Any root of $1$ is $1$ .

$- 1 \cdot 1 - \sqrt{- 100} - \sqrt{121} + \sqrt{- 1}$

Step 1.2

Multiply $- 1$ by $1$ .

$- 1 - \sqrt{- 100} - \sqrt{121} + \sqrt{- 1}$

Step 1.3

Rewrite $- 100$ as $- 1 (100)$ .

$- 1 - \sqrt{- 1 (100)} - \sqrt{121} + \sqrt{- 1}$

Step 1.4

Rewrite $\sqrt{- 1 (100)}$ as $\sqrt{- 1} \cdot \sqrt{100}$ .

$- 1 - (\sqrt{- 1} \cdot \sqrt{100}) - \sqrt{121} + \sqrt{- 1}$

Step 1.5

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

$- 1 - (i \cdot \sqrt{100}) - \sqrt{121} + \sqrt{- 1}$

Step 1.6

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

$- 1 - (i \cdot \sqrt{10^{2}}) - \sqrt{121} + \sqrt{- 1}$

Step 1.7

Pull terms out from under the radical, assuming positive real numbers.

$- 1 - (i \cdot 10) - \sqrt{121} + \sqrt{- 1}$

Step 1.8

Move $10$ to the left of $i$ .

$- 1 - (10 \cdot i) - \sqrt{121} + \sqrt{- 1}$

Step 1.9

Multiply $10$ by $- 1$ .

$- 1 - 10 i - \sqrt{121} + \sqrt{- 1}$

Step 1.10

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

$- 1 - 10 i - \sqrt{11^{2}} + \sqrt{- 1}$

Step 1.11

Pull terms out from under the radical, assuming positive real numbers.

$- 1 - 10 i - 1 \cdot 11 + \sqrt{- 1}$

Step 1.12

Multiply $- 1$ by $11$ .

$- 1 - 10 i - 11 + \sqrt{- 1}$

Step 1.13

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

$- 1 - 10 i - 11 + i$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $11$ from $- 1$ .

$- 12 - 10 i + i$

Step 2.2

Add $- 10 i$ and $i$ .

$- 12 - 9 i$