Simplify the Radical Expression -x square root of 200x^2-9 square root of 2x^4

$- x \sqrt{200 x^{2}} - 9 \sqrt{2 x^{4}}$

Step 1

Simplify each term.

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

Factor $100$ out of $200$ .

$- x \sqrt{100 (2) x^{2}} - 9 \sqrt{2 x^{4}}$

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

$- x \sqrt{10^{2} \cdot 2 x^{2}} - 9 \sqrt{2 x^{4}}$

Move $2$ .

$- x \sqrt{10^{2} x^{2} \cdot 2} - 9 \sqrt{2 x^{4}}$

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

$- x \sqrt{{(10 x)}^{2} \cdot 2} - 9 \sqrt{2 x^{4}}$

Pull terms out from under the radical.

$- x (| 10 x | \sqrt{2}) - 9 \sqrt{2 x^{4}}$

Remove non-negative terms from the absolute value.

$- x (10 | x | \sqrt{2}) - 9 \sqrt{2 x^{4}}$

Multiply $10$ by $- 1$ .

$- 10 x (| x | \sqrt{2}) - 9 \sqrt{2 x^{4}}$

Rewrite $2 x^{4}$ as ${(x^{2})}^{2} \cdot 2$ .

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

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

Reorder $2$ and ${(x^{2})}^{2}$ .

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

Pull terms out from under the radical.

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

Remove non-negative terms from the absolute value.

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

Step 2

Reorder factors in $- 10 x (| x | \sqrt{2}) - 9 x^{2} \sqrt{2}$ .

$- 10 x | x | \sqrt{2} - 9 x^{2} \sqrt{2}$