Simplify the Radical Expression 6x square root of 9x^3

$6 x \sqrt{9 x^{3}}$

Rewrite $9 x^{3}$ as ${(3 x)}^{2} x$ .

Rewrite $9$ as $3^{2}$ .

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

Factor out $x^{2}$ .

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

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

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

Pull terms out from under the radical.

$6 x (| 3 x | \sqrt{x})$

Remove non-negative terms from the absolute value.

$6 x (3 | x | \sqrt{x})$

Multiply $3$ by $6$ .

$18 x (| x | \sqrt{x})$

Reorder factors in $18 x (| x | \sqrt{x})$ .

$18 x | x | \sqrt{x}$