Algebra Examples

$\sqrt{- 2} + \sqrt{- 18}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $- 2$ as $- 1 (2)$ .

$\sqrt{- 1 (2)} + \sqrt{- 18}$

Step 1.2

Rewrite $\sqrt{- 1 (2)}$ as $\sqrt{- 1} \cdot \sqrt{2}$ .

$\sqrt{- 1} \cdot \sqrt{2} + \sqrt{- 18}$

Step 1.3

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

$i \cdot \sqrt{2} + \sqrt{- 18}$

Step 1.4

Rewrite $- 18$ as $- 1 (18)$ .

$i \sqrt{2} + \sqrt{- 1 (18)}$

Step 1.5

Rewrite $\sqrt{- 1 (18)}$ as $\sqrt{- 1} \cdot \sqrt{18}$ .

$i \sqrt{2} + \sqrt{- 1} \cdot \sqrt{18}$

Step 1.6

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

$i \sqrt{2} + i \cdot \sqrt{18}$

Step 1.7

Rewrite $18$ as $3^{2} \cdot 2$ .

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Step 1.7.1

Factor $9$ out of $18$ .

$i \sqrt{2} + i \cdot \sqrt{9 (2)}$

Step 1.7.2

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

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

Step 1.8

Pull terms out from under the radical.

$i \sqrt{2} + i \cdot (3 \sqrt{2})$

Step 1.9

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

$i \sqrt{2} + 3 i \sqrt{2}$

Step 2

Add $i \sqrt{2}$ and $3 i \sqrt{2}$ .

$4 i \sqrt{2}$