Algebra Examples

$\sqrt{- 72} + 4$

Step 1

Simplify each term.

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Step 1.1

Rewrite $- 72$ as $- 1 (72)$ .

$\sqrt{- 1 (72)} + 4$

Step 1.2

Rewrite $\sqrt{- 1 (72)}$ as $\sqrt{- 1} \cdot \sqrt{72}$ .

$\sqrt{- 1} \cdot \sqrt{72} + 4$

Step 1.3

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

$i \cdot \sqrt{72} + 4$

Step 1.4

Rewrite $72$ as $6^{2} \cdot 2$ .

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Step 1.4.1

Factor $36$ out of $72$ .

$i \cdot \sqrt{36 (2)} + 4$

Step 1.4.2

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

$i \cdot \sqrt{6^{2} \cdot 2} + 4$

Step 1.5

Pull terms out from under the radical.

$i \cdot (6 \sqrt{2}) + 4$

Step 1.6

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

$6 i \sqrt{2} + 4$

Step 2

Reorder $6 i \sqrt{2}$ and $4$ .

$4 + 6 i \sqrt{2}$