Simplify square root of 20a^5

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

Step 1

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

Factor $4$ out of $20$ .

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

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

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

Factor out $a^{4}$ .

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

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

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

Move $5$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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