Algebra Examples

$- \sqrt{1} + \sqrt{- 81} - \sqrt{16} - \sqrt{- 1}$

Step 1

Simplify each term.

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Step 1.1

Any root of $1$ is $1$ .

$- 1 \cdot 1 + \sqrt{- 81} - \sqrt{16} - \sqrt{- 1}$

Step 1.2

Multiply $- 1$ by $1$ .

$- 1 + \sqrt{- 81} - \sqrt{16} - \sqrt{- 1}$

Step 1.3

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

$- 1 + \sqrt{- 1 (81)} - \sqrt{16} - \sqrt{- 1}$

Step 1.4

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

$- 1 + \sqrt{- 1} \cdot \sqrt{81} - \sqrt{16} - \sqrt{- 1}$

Step 1.5

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

$- 1 + i \cdot \sqrt{81} - \sqrt{16} - \sqrt{- 1}$

Step 1.6

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

$- 1 + i \cdot \sqrt{9^{2}} - \sqrt{16} - \sqrt{- 1}$

Step 1.7

Pull terms out from under the radical.

$- 1 + i \cdot | 9 | - \sqrt{16} - \sqrt{- 1}$

Step 1.8

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

$- 1 + i \cdot 9 - \sqrt{16} - \sqrt{- 1}$

Step 1.9

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

$- 1 + 9 \cdot i - \sqrt{16} - \sqrt{- 1}$

Step 1.10

Rewrite $16$ as $4^{2}$ .

$- 1 + 9 i - \sqrt{4^{2}} - \sqrt{- 1}$

Step 1.11

Pull terms out from under the radical.

$- 1 + 9 i - | 4 | - \sqrt{- 1}$

Step 1.12

The absolute value is the distance between a number and zero. The distance between $0$ and $4$ is $4$ .

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

Step 1.13

Multiply $- 1$ by $4$ .

$- 1 + 9 i - 4 - \sqrt{- 1}$

Step 1.14

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

$- 1 + 9 i - 4 - i$

Step 2

Subtract $4$ from $- 1$ .

$- 5 + 9 i - i$

Step 3

Subtract $i$ from $9 i$ .

$- 5 + 8 i$