Algebra Examples

$\sqrt{- 108} - \sqrt{- 3}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Rewrite $- 108$ as $- 1 (108)$ .

$\sqrt{- 1 (108)} - \sqrt{- 3}$

Step 1.2

Rewrite $\sqrt{- 1 (108)}$ as $\sqrt{- 1} \cdot \sqrt{108}$ .

$\sqrt{- 1} \cdot \sqrt{108} - \sqrt{- 3}$

Step 1.3

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

$i \cdot \sqrt{108} - \sqrt{- 3}$

Step 1.4

Rewrite $108$ as $6^{2} \cdot 3$ .

Tap for more steps...

Step 1.4.1

Factor $36$ out of $108$ .

$i \cdot \sqrt{36 (3)} - \sqrt{- 3}$

Step 1.4.2

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

$i \cdot \sqrt{6^{2} \cdot 3} - \sqrt{- 3}$

Step 1.5

Pull terms out from under the radical.

$i \cdot (6 \sqrt{3}) - \sqrt{- 3}$

Step 1.6

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

$6 \cdot i \sqrt{3} - \sqrt{- 3}$

Step 1.7

Rewrite $- 3$ as $- 1 (3)$ .

$6 i \sqrt{3} - \sqrt{- 1 (3)}$

Step 1.8

Rewrite $\sqrt{- 1 (3)}$ as $\sqrt{- 1} \cdot \sqrt{3}$ .

$6 i \sqrt{3} - (\sqrt{- 1} \cdot \sqrt{3})$

Step 1.9

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

$6 i \sqrt{3} - i \sqrt{3}$

Step 2

Subtract $i \sqrt{3}$ from $6 i \sqrt{3}$ .

$5 i \sqrt{3}$