Simplify 3 square root of -1000

$3 \sqrt{- 1000}$

Step 1

Rewrite $- 1000$ as $- 1 (1000)$ .

$3 \sqrt{- 1 (1000)}$

Step 2

Rewrite $\sqrt{- 1 (1000)}$ as $\sqrt{- 1} \cdot \sqrt{1000}$ .

$3 (\sqrt{- 1} \cdot \sqrt{1000})$

Step 3

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

$3 (i \cdot \sqrt{1000})$

Step 4

Rewrite $1000$ as $10^{2} \cdot 10$ .

Factor $100$ out of $1000$ .

$3 (i \cdot \sqrt{100 (10)})$

Rewrite $100$ as $10^{2}$ .

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

Step 5

Pull terms out from under the radical.

$3 (i \cdot (10 \sqrt{10}))$

Step 6

Simplify the expression.

Move $10$ to the left of $i$ .

$3 (10 \cdot i \sqrt{10})$

Multiply $10$ by $3$ .

$30 i \sqrt{10}$