Simplify square root of 20a^2b^4

$\sqrt{20 a^{2} b^{4}}$

Step 1

Rewrite $20 a^{2} b^{4}$ as ${(2 a b^{2})}^{2} \cdot 5$ .

Factor $4$ out of $20$ .

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

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

$\sqrt{2^{2} \cdot 5 a^{2} b^{4}}$

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

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

Move $5$ .

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

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

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

Step 2

Pull terms out from under the radical.

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