Basic Math Examples

$(10 + \sqrt{- 9}) + (8 + \sqrt{- 81})$

Step 1

Remove parentheses.

$10 + \sqrt{- 9} + 8 + \sqrt{- 81}$

Step 2

Simplify each term.

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Step 2.1

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

$10 + \sqrt{- 1 (9)} + 8 + \sqrt{- 81}$

Step 2.2

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

$10 + \sqrt{- 1} \cdot \sqrt{9} + 8 + \sqrt{- 81}$

Step 2.3

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

$10 + i \cdot \sqrt{9} + 8 + \sqrt{- 81}$

Step 2.4

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

$10 + i \cdot \sqrt{3^{2}} + 8 + \sqrt{- 81}$

Step 2.5

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

$10 + i \cdot 3 + 8 + \sqrt{- 81}$

Step 2.6

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

$10 + 3 \cdot i + 8 + \sqrt{- 81}$

Step 2.7

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

$10 + 3 i + 8 + \sqrt{- 1 (81)}$

Step 2.8

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

$10 + 3 i + 8 + \sqrt{- 1} \cdot \sqrt{81}$

Step 2.9

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

$10 + 3 i + 8 + i \cdot \sqrt{81}$

Step 2.10

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

$10 + 3 i + 8 + i \cdot \sqrt{9^{2}}$

Step 2.11

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

$10 + 3 i + 8 + i \cdot 9$

Step 2.12

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

$10 + 3 i + 8 + 9 i$

Step 3

Simplify by adding terms.

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Step 3.1

Add $10$ and $8$ .

$18 + 3 i + 9 i$

Step 3.2

Add $3 i$ and $9 i$ .

$18 + 12 i$