Simplify -x^2 square root of 200x^3+x^3 square root of 72x

$- x^{2} \sqrt{200 x^{3}} + x^{3} \sqrt{72 x}$

Step 1

Simplify each term.

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

Factor $100$ out of $200$ .

$- x^{2} \sqrt{100 (2) x^{3}} + x^{3} \sqrt{72 x}$

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

$- x^{2} \sqrt{10^{2} \cdot 2 x^{3}} + x^{3} \sqrt{72 x}$

Factor out $x^{2}$ .

$- x^{2} \sqrt{10^{2} \cdot 2 (x^{2} x)} + x^{3} \sqrt{72 x}$

Move $2$ .

$- x^{2} \sqrt{10^{2} x^{2} \cdot 2 x} + x^{3} \sqrt{72 x}$

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

$- x^{2} \sqrt{{(10 x)}^{2} \cdot 2 x} + x^{3} \sqrt{72 x}$

Add parentheses.

$- x^{2} \sqrt{{(10 x)}^{2} \cdot (2 x)} + x^{3} \sqrt{72 x}$

Pull terms out from under the radical.

$- x^{2} (10 x \sqrt{2 x}) + x^{3} \sqrt{72 x}$

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

$- (x \cdot x^{2}) (10 \sqrt{2 x}) + x^{3} \sqrt{72 x}$

Multiply $x$ by $x^{2}$ .

Raise $x$ to the power of $1$ .

$- (x^{1} x^{2}) (10 \sqrt{2 x}) + x^{3} \sqrt{72 x}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- x^{1 + 2} (10 \sqrt{2 x}) + x^{3} \sqrt{72 x}$

Add $1$ and $2$ .

$- x^{3} (10 \sqrt{2 x}) + x^{3} \sqrt{72 x}$

Multiply $10$ by $- 1$ .

$- 10 x^{3} \sqrt{2 x} + x^{3} \sqrt{72 x}$

Rewrite $72 x$ as $6^{2} \cdot (2 x)$ .

Factor $36$ out of $72$ .

$- 10 x^{3} \sqrt{2 x} + x^{3} \sqrt{36 (2) x}$

Rewrite $36$ as $6^{2}$ .

$- 10 x^{3} \sqrt{2 x} + x^{3} \sqrt{6^{2} \cdot 2 x}$

Add parentheses.

$- 10 x^{3} \sqrt{2 x} + x^{3} \sqrt{6^{2} \cdot (2 x)}$

Pull terms out from under the radical.

$- 10 x^{3} \sqrt{2 x} + x^{3} (6 \sqrt{2 x})$

Rewrite using the commutative property of multiplication.

$- 10 x^{3} \sqrt{2 x} + 6 x^{3} \sqrt{2 x}$

Step 2

Add $- 10 x^{3} \sqrt{2 x}$ and $6 x^{3} \sqrt{2 x}$ .

$- 4 x^{3} \sqrt{2 x}$