Simplify 3x^3 square root of 72x^6y^2

$3 x^{3} \sqrt{72 x^{6} y^{2}}$

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

Factor $36$ out of $72$ .

$3 x^{3} \sqrt{36 (2) x^{6} y^{2}}$

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

$3 x^{3} \sqrt{6^{2} \cdot 2 x^{6} y^{2}}$

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

$3 x^{3} \sqrt{6^{2} \cdot 2 {(x^{3})}^{2} y^{2}}$

Move $2$ .

$3 x^{3} \sqrt{6^{2} {(x^{3})}^{2} y^{2} \cdot 2}$

Rewrite $6^{2} {(x^{3})}^{2} y^{2}$ as ${(6 x^{3} y)}^{2}$ .

$3 x^{3} \sqrt{{(6 x^{3} y)}^{2} \cdot 2}$

Pull terms out from under the radical.

$3 x^{3} (6 x^{3} y \sqrt{2})$

Multiply $x^{3}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$3 (x^{3} x^{3}) (6 y \sqrt{2})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 x^{3 + 3} (6 y \sqrt{2})$

Add $3$ and $3$ .

$3 x^{6} (6 y \sqrt{2})$

Multiply $6$ by $3$ .

$18 x^{6} y \sqrt{2}$