Algebra Examples

$\frac{2}{3} \sqrt{- 72}$

Step 1

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

$\frac{2}{3} \cdot \sqrt{- 1 (72)}$

Step 2

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

$\frac{2}{3} \cdot (\sqrt{- 1} \cdot \sqrt{72})$

Step 3

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

$\frac{2}{3} \cdot (i \cdot \sqrt{72})$

Step 4

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

Tap for more steps...

Step 4.1

Factor $36$ out of $72$ .

$\frac{2}{3} \cdot (i \cdot \sqrt{36 (2)})$

Step 4.2

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

$\frac{2}{3} \cdot (i \cdot \sqrt{6^{2} \cdot 2})$

Step 5

Pull terms out from under the radical.

$\frac{2}{3} \cdot (i \cdot (6 \sqrt{2}))$

Step 6

Cancel the common factor of $3$ .

Tap for more steps...

Step 6.1

Factor $3$ out of $i \cdot (6 \sqrt{2})$ .

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

Step 6.2

Cancel the common factor.

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

Step 6.3

Rewrite the expression.

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

Step 7

Multiply $2$ by $2$ .

$4 i \sqrt{2}$