Simplify square root of 40a^3b^4

$\sqrt{40 a^{3} b^{4}}$

Step 1

Rewrite $40 a^{3} b^{4}$ as ${(2 a b^{2})}^{2} \cdot (10 a)$ .

Factor $4$ out of $40$ .

$\sqrt{4 (10) a^{3} b^{4}}$

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

$\sqrt{2^{2} \cdot 10 a^{3} b^{4}}$

Factor out $a^{2}$ .

$\sqrt{2^{2} \cdot 10 (a^{2} a) b^{4}}$

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

$\sqrt{2^{2} \cdot 10 (a^{2} a) {(b^{2})}^{2}}$

Move $a$ .

$\sqrt{2^{2} \cdot 10 (a^{2}) {(b^{2})}^{2} a}$

Move $10$ .

$\sqrt{2^{2} (a^{2}) {(b^{2})}^{2} \cdot 10 a}$

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

$\sqrt{{(2 a b^{2})}^{2} \cdot 10 a}$

Add parentheses.

$\sqrt{{(2 a b^{2})}^{2} \cdot (10 a)}$

Step 2

Pull terms out from under the radical.

$2 a b^{2} \sqrt{10 a}$