Simplify square root of a^3b^5c^3

$\sqrt{a^{3} b^{5} c^{3}}$

Step 1

Rewrite $a^{3} b^{5} c^{3}$ as ${(a b^{2} c)}^{2} (a b c)$ .

Factor out $a^{2}$ .

$\sqrt{a^{2} a b^{5} c^{3}}$

Factor out $b^{4}$ .

$\sqrt{a^{2} a (b^{4} b) c^{3}}$

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

$\sqrt{a^{2} a ({(b^{2})}^{2} b) c^{3}}$

Factor out $c^{2}$ .

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

Move $b$ .

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

Move $a$ .

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

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

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

Add parentheses.

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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