Simplify the Radical Expression 9 square root of 200x^3+x square root of 2x

$9 \sqrt{200 x^{3}} + x \sqrt{2 x}$

Step 1

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

Factor $100$ out of $200$ .

$9 \sqrt{100 (2) x^{3}} + x \sqrt{2 x}$

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

$9 \sqrt{10^{2} \cdot 2 x^{3}} + x \sqrt{2 x}$

Factor out $x^{2}$ .

$9 \sqrt{10^{2} \cdot 2 (x^{2} x)} + x \sqrt{2 x}$

Move $2$ .

$9 \sqrt{10^{2} x^{2} \cdot 2 x} + x \sqrt{2 x}$

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

$9 \sqrt{{(10 x)}^{2} \cdot 2 x} + x \sqrt{2 x}$

Add parentheses.

$9 \sqrt{{(10 x)}^{2} \cdot (2 x)} + x \sqrt{2 x}$

Step 2

Pull terms out from under the radical.

$9 (| 10 x | \sqrt{2 x}) + x \sqrt{2 x}$

Step 3

Remove non-negative terms from the absolute value.

$9 (10 | x | \sqrt{2 x}) + x \sqrt{2 x}$

Step 4

Multiply $10$ by $9$ .

$90 | x | \sqrt{2 x} + x \sqrt{2 x}$