Simplify square root of -75x^5

$\sqrt{- 75 x^{5}}$

Step 1

Rewrite $- 75 x^{5}$ as ${(5 x^{2})}^{2} \cdot (- 3 x)$ .

Factor $25$ out of $- 75$ .

$\sqrt{25 (- 3) x^{5}}$

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} \cdot - 3 x^{5}}$

Factor out $x^{4}$ .

$\sqrt{5^{2} \cdot - 3 (x^{4} x)}$

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$\sqrt{5^{2} \cdot - 3 ({(x^{2})}^{2} x)}$

Move $- 3$ .

$\sqrt{5^{2} {(x^{2})}^{2} \cdot - 3 x}$

Rewrite $5^{2} {(x^{2})}^{2}$ as ${(5 x^{2})}^{2}$ .

$\sqrt{{(5 x^{2})}^{2} \cdot - 3 x}$

Add parentheses.

$\sqrt{{(5 x^{2})}^{2} \cdot (- 3 x)}$

Step 2

Pull terms out from under the radical.

$5 x^{2} \sqrt{- 3 x}$