Simplify square root of 60a^3

$\sqrt{60 a^{3}}$

Rewrite $60 a^{3}$ as ${(2 a)}^{2} \cdot (15 a)$ .

Factor $4$ out of $60$ .

$\sqrt{4 (15) a^{3}}$

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

$\sqrt{2^{2} \cdot 15 a^{3}}$

Factor out $a^{2}$ .

$\sqrt{2^{2} \cdot 15 (a^{2} a)}$

Move $15$ .

$\sqrt{2^{2} a^{2} \cdot 15 a}$

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

$\sqrt{{(2 a)}^{2} \cdot 15 a}$

Add parentheses.

$\sqrt{{(2 a)}^{2} \cdot (15 a)}$

Pull terms out from under the radical.

$2 a \sqrt{15 a}$