Simplify 2/5 square root of -225

$\frac{2}{5} \sqrt{- 225}$

Step 1

Rewrite $- 225$ as $- 1 (225)$ .

$\frac{2}{5} \cdot \sqrt{- 1 (225)}$

Step 2

Rewrite $\sqrt{- 1 (225)}$ as $\sqrt{- 1} \cdot \sqrt{225}$ .

$\frac{2}{5} \cdot (\sqrt{- 1} \cdot \sqrt{225})$

Step 3

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

$\frac{2}{5} \cdot (i \cdot \sqrt{225})$

Step 4

Write the expression using exponents.

Rewrite $225$ as $15^{2}$ .

$\frac{2}{5} \cdot (i \cdot \sqrt{15^{2}})$

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

$\frac{2}{5} \cdot (i \cdot 15)$

Step 5

Cancel the common factor of $5$ .

Factor $5$ out of $i \cdot 15$ .

$\frac{2}{5} \cdot (5 (i \cdot 3))$

Cancel the common factor.

$\frac{2}{5} \cdot (5 (i \cdot 3))$

Rewrite the expression.

$2 \cdot (i \cdot 3)$

Step 6

Multiply $3$ by $2$ .

$6 i$