Simplify -5x^2 square root of 2x+x square root of 200x^3

$- 5 x^{2} \sqrt{2 x} + x \sqrt{200 x^{3}}$

Step 1

Simplify each term.

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

Factor $100$ out of $200$ .

$- 5 x^{2} \sqrt{2 x} + x \sqrt{100 (2) x^{3}}$

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

$- 5 x^{2} \sqrt{2 x} + x \sqrt{10^{2} \cdot 2 x^{3}}$

Factor out $x^{2}$ .

$- 5 x^{2} \sqrt{2 x} + x \sqrt{10^{2} \cdot 2 (x^{2} x)}$

Move $2$ .

$- 5 x^{2} \sqrt{2 x} + x \sqrt{10^{2} x^{2} \cdot 2 x}$

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

$- 5 x^{2} \sqrt{2 x} + x \sqrt{{(10 x)}^{2} \cdot 2 x}$

Add parentheses.

$- 5 x^{2} \sqrt{2 x} + x \sqrt{{(10 x)}^{2} \cdot (2 x)}$

Pull terms out from under the radical.

$- 5 x^{2} \sqrt{2 x} + x (10 x \sqrt{2 x})$

Rewrite using the commutative property of multiplication.

$- 5 x^{2} \sqrt{2 x} + 10 x (x \sqrt{2 x})$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$- 5 x^{2} \sqrt{2 x} + 10 (x \cdot x) \sqrt{2 x}$

Multiply $x$ by $x$ .

$- 5 x^{2} \sqrt{2 x} + 10 x^{2} \sqrt{2 x}$

Step 2

Add $- 5 x^{2} \sqrt{2 x}$ and $10 x^{2} \sqrt{2 x}$ .

$5 x^{2} \sqrt{2 x}$