Algebra Examples

$\sqrt{- 36} + \sqrt{- 64}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $- 36$ as $- 1 (36)$ .

$\sqrt{- 1 (36)} + \sqrt{- 64}$

Step 1.2

Rewrite $\sqrt{- 1 (36)}$ as $\sqrt{- 1} \cdot \sqrt{36}$ .

$\sqrt{- 1} \cdot \sqrt{36} + \sqrt{- 64}$

Step 1.3

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

$i \cdot \sqrt{36} + \sqrt{- 64}$

Step 1.4

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

$i \cdot \sqrt{6^{2}} + \sqrt{- 64}$

Step 1.5

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

$i \cdot 6 + \sqrt{- 64}$

Step 1.6

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

$6 \cdot i + \sqrt{- 64}$

Step 1.7

Rewrite $- 64$ as $- 1 (64)$ .

$6 i + \sqrt{- 1 (64)}$

Step 1.8

Rewrite $\sqrt{- 1 (64)}$ as $\sqrt{- 1} \cdot \sqrt{64}$ .

$6 i + \sqrt{- 1} \cdot \sqrt{64}$

Step 1.9

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

$6 i + i \cdot \sqrt{64}$

Step 1.10

Rewrite $64$ as $8^{2}$ .

$6 i + i \cdot \sqrt{8^{2}}$

Step 1.11

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

$6 i + i \cdot 8$

Step 1.12

Move $8$ to the left of $i$ .

$6 i + 8 i$

Step 2

Add $6 i$ and $8 i$ .

$14 i$