Simplify square root of 56a^2b^4c^5

$\sqrt{56 a^{2} b^{4} c^{5}}$

Step 1

Rewrite $56 a^{2} b^{4} c^{5}$ as ${(2 a b^{2} c^{2})}^{2} \cdot (14 c)$ .

Factor $4$ out of $56$ .

$\sqrt{4 (14) a^{2} b^{4} c^{5}}$

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

$\sqrt{2^{2} \cdot 14 a^{2} b^{4} c^{5}}$

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

$\sqrt{2^{2} \cdot 14 a^{2} {(b^{2})}^{2} c^{5}}$

Factor out $c^{4}$ .

$\sqrt{2^{2} \cdot 14 a^{2} {(b^{2})}^{2} (c^{4} c)}$

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

$\sqrt{2^{2} \cdot 14 a^{2} {(b^{2})}^{2} ({(c^{2})}^{2} c)}$

Move $14$ .

$\sqrt{2^{2} a^{2} {(b^{2})}^{2} {(c^{2})}^{2} \cdot 14 c}$

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

$\sqrt{{(2 a b^{2} c^{2})}^{2} \cdot 14 c}$

Add parentheses.

$\sqrt{{(2 a b^{2} c^{2})}^{2} \cdot (14 c)}$

Step 2

Pull terms out from under the radical.

$2 a b^{2} c^{2} \sqrt{14 c}$