Simplify square root of 20x^5

$\sqrt{20 x^{5}}$

Step 1

Rewrite $20 x^{5}$ as ${(2 x^{2})}^{2} \cdot (5 x)$ .

Factor $4$ out of $20$ .

$\sqrt{4 (5) x^{5}}$

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

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

Factor out $x^{4}$ .

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

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

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

Move $5$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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