Simplify 3/4 square root of -80

$\frac{3}{4} \sqrt{- 80}$

Step 1

Rewrite $- 80$ as $- 1 (80)$ .

$\frac{3}{4} \cdot \sqrt{- 1 (80)}$

Step 2

Rewrite $\sqrt{- 1 (80)}$ as $\sqrt{- 1} \cdot \sqrt{80}$ .

$\frac{3}{4} \cdot (\sqrt{- 1} \cdot \sqrt{80})$

Step 3

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

$\frac{3}{4} \cdot (i \cdot \sqrt{80})$

Step 4

Rewrite $80$ as $4^{2} \cdot 5$ .

Factor $16$ out of $80$ .

$\frac{3}{4} \cdot (i \cdot \sqrt{16 (5)})$

Rewrite $16$ as $4^{2}$ .

$\frac{3}{4} \cdot (i \cdot \sqrt{4^{2} \cdot 5})$

Step 5

Pull terms out from under the radical.

$\frac{3}{4} \cdot (i \cdot (4 \sqrt{5}))$

Step 6

Cancel the common factor of $4$ .

Factor $4$ out of $i \cdot (4 \sqrt{5})$ .

$\frac{3}{4} \cdot (4 (i \cdot (\sqrt{5})))$

Cancel the common factor.

$\frac{3}{4} \cdot (4 (i \cdot (\sqrt{5})))$

Rewrite the expression.

$3 \cdot (i \cdot (\sqrt{5}))$

$3 i \sqrt{5}$