Simplify the Radical Expression 3x square root of 200x^3

$3 x \sqrt{200 x^{3}}$

Rewrite $200 x^{3}$ as ${(10 x)}^{2} \cdot (2 x)$ .

Factor $100$ out of $200$ .

$3 x \sqrt{100 (2) x^{3}}$

Rewrite $100$ as $10^{2}$ .

$3 x \sqrt{10^{2} \cdot 2 x^{3}}$

Factor out $x^{2}$ .

$3 x \sqrt{10^{2} \cdot 2 (x^{2} x)}$

Move $2$ .

$3 x \sqrt{10^{2} x^{2} \cdot 2 x}$

Rewrite $10^{2} x^{2}$ as ${(10 x)}^{2}$ .

$3 x \sqrt{{(10 x)}^{2} \cdot 2 x}$

Add parentheses.

$3 x \sqrt{{(10 x)}^{2} \cdot (2 x)}$

Pull terms out from under the radical.

$3 x (| 10 x | \sqrt{2 x})$

Remove non-negative terms from the absolute value.

$3 x (10 | x | \sqrt{2 x})$

Multiply $10$ by $3$ .

$30 x (| x | \sqrt{2 x})$

Reorder factors in $30 x (| x | \sqrt{2 x})$ .

$30 x | x | \sqrt{2 x}$