Algebra Examples

$\sqrt{- 9} + \sqrt{- 25} - \sqrt{- 5}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $- 9$ as $- 1 (9)$ .

$\sqrt{- 1 (9)} + \sqrt{- 25} - \sqrt{- 5}$

Step 1.2

Rewrite $\sqrt{- 1 (9)}$ as $\sqrt{- 1} \cdot \sqrt{9}$ .

$\sqrt{- 1} \cdot \sqrt{9} + \sqrt{- 25} - \sqrt{- 5}$

Step 1.3

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

$i \cdot \sqrt{9} + \sqrt{- 25} - \sqrt{- 5}$

Step 1.4

Rewrite $9$ as $3^{2}$ .

$i \cdot \sqrt{3^{2}} + \sqrt{- 25} - \sqrt{- 5}$

Step 1.5

Pull terms out from under the radical.

$i \cdot | 3 | + \sqrt{- 25} - \sqrt{- 5}$

Step 1.6

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

$i \cdot 3 + \sqrt{- 25} - \sqrt{- 5}$

Step 1.7

Move $3$ to the left of $i$ .

$3 \cdot i + \sqrt{- 25} - \sqrt{- 5}$

Step 1.8

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

$3 i + \sqrt{- 1 (25)} - \sqrt{- 5}$

Step 1.9

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

$3 i + \sqrt{- 1} \cdot \sqrt{25} - \sqrt{- 5}$

Step 1.10

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

$3 i + i \cdot \sqrt{25} - \sqrt{- 5}$

Step 1.11

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

$3 i + i \cdot \sqrt{5^{2}} - \sqrt{- 5}$

Step 1.12

Pull terms out from under the radical.

$3 i + i \cdot | 5 | - \sqrt{- 5}$

Step 1.13

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

$3 i + i \cdot 5 - \sqrt{- 5}$

Step 1.14

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

$3 i + 5 \cdot i - \sqrt{- 5}$

Step 1.15

Rewrite $- 5$ as $- 1 (5)$ .

$3 i + 5 i - \sqrt{- 1 (5)}$

Step 1.16

Rewrite $\sqrt{- 1 (5)}$ as $\sqrt{- 1} \cdot \sqrt{5}$ .

$3 i + 5 i - (\sqrt{- 1} \cdot \sqrt{5})$

Step 1.17

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

$3 i + 5 i - i \sqrt{5}$

Step 2

Add $3 i$ and $5 i$ .

$8 i - i \sqrt{5}$