Simplify square root of 72a^3b^4c^5

$\sqrt{72 a^{3}} b^{4} c^{5}$

Rewrite $72 a^{3}$ as ${(6 a)}^{2} \cdot (2 a)$ .

Factor $36$ out of $72$ .

$\sqrt{36 (2) a^{3}} b^{4} c^{5}$

Rewrite $36$ as $6^{2}$ .

$\sqrt{6^{2} \cdot 2 a^{3}} b^{4} c^{5}$

Factor out $a^{2}$ .

$\sqrt{6^{2} \cdot 2 (a^{2} a)} b^{4} c^{5}$

Move $2$ .

$\sqrt{6^{2} a^{2} \cdot 2 a} b^{4} c^{5}$

Rewrite $6^{2} a^{2}$ as ${(6 a)}^{2}$ .

$\sqrt{{(6 a)}^{2} \cdot 2 a} b^{4} c^{5}$

Add parentheses.

$\sqrt{{(6 a)}^{2} \cdot (2 a)} b^{4} c^{5}$

$\sqrt{{(6 a)}^{2} \cdot (2 a)} b^{4} c^{5}$

Pull terms out from under the radical.

$6 a \sqrt{2 a} b^{4} c^{5}$

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