Simplify 3/5 square root of -100/9

$\frac{3}{5} \sqrt{- \frac{100}{9}}$

Step 1

Rewrite $- \frac{100}{9}$ as ${(\frac{10 i}{3})}^{2}$ .

$\frac{3}{5} \cdot \sqrt{{(\frac{10 i}{3})}^{2}}$

Step 2

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

$\frac{3}{5} \cdot \frac{10 i}{3}$

Step 3

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{5} \cdot \frac{10 i}{3}$

Rewrite the expression.

$\frac{1}{5} \cdot (10 i)$

Step 4

Cancel the common factor of $5$ .

Factor $5$ out of $10 i$ .

$\frac{1}{5} \cdot (5 (2 i))$

Cancel the common factor.

$\frac{1}{5} \cdot (5 (2 i))$

Rewrite the expression.

$2 i$