Simplify 10 square root of -81/25

$10 \sqrt{\frac{- 81}{25}}$

Step 1

Move the negative in front of the fraction.

$10 \sqrt{- \frac{81}{25}}$

Step 2

Rewrite $- \frac{81}{25}$ as ${(\frac{9 i}{5})}^{2}$ .

$10 \sqrt{{(\frac{9 i}{5})}^{2}}$

Step 3

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

$10 \frac{9 i}{5}$

Step 4

Cancel the common factor of $5$ .

Factor $5$ out of $10$ .

$5 (2) \frac{9 i}{5}$

Cancel the common factor.

$5 \cdot 2 \frac{9 i}{5}$

Rewrite the expression.

$2 (9 i)$

Step 5

Multiply $9$ by $2$ .

$18 i$