Simplify -5x square root of 192x^3+ square root of 3x^5

$- 5 x \sqrt{192 x^{3}} + \sqrt{3 x^{5}}$

Simplify each term.

Rewrite $192 x^{3}$ as ${(8 x)}^{2} \cdot (3 x)$ .

Factor $64$ out of $192$ .

$- 5 x \sqrt{64 (3) x^{3}} + \sqrt{3 x^{5}}$

Rewrite $64$ as $8^{2}$ .

$- 5 x \sqrt{8^{2} \cdot 3 x^{3}} + \sqrt{3 x^{5}}$

Factor out $x^{2}$ .

$- 5 x \sqrt{8^{2} \cdot 3 (x^{2} x)} + \sqrt{3 x^{5}}$

Move $3$ .

$- 5 x \sqrt{8^{2} x^{2} \cdot 3 x} + \sqrt{3 x^{5}}$

Rewrite $8^{2} x^{2}$ as ${(8 x)}^{2}$ .

$- 5 x \sqrt{{(8 x)}^{2} \cdot 3 x} + \sqrt{3 x^{5}}$

Add parentheses.

$- 5 x \sqrt{{(8 x)}^{2} \cdot (3 x)} + \sqrt{3 x^{5}}$

Pull terms out from under the radical.

$- 5 x (8 x \sqrt{3 x}) + \sqrt{3 x^{5}}$

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

Move $x$ .

$- 5 (x \cdot x) (8 \sqrt{3 x}) + \sqrt{3 x^{5}}$

Multiply $x$ by $x$ .

$- 5 x^{2} (8 \sqrt{3 x}) + \sqrt{3 x^{5}}$

Multiply $8$ by $- 5$ .

$- 40 x^{2} \sqrt{3 x} + \sqrt{3 x^{5}}$

Rewrite $3 x^{5}$ as ${(x^{2})}^{2} \cdot (3 x)$ .

Factor out $x^{4}$ .

$- 40 x^{2} \sqrt{3 x} + \sqrt{3 (x^{4} x)}$

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

$- 40 x^{2} \sqrt{3 x} + \sqrt{3 ({(x^{2})}^{2} x)}$

Reorder $3$ and ${(x^{2})}^{2}$ .

$- 40 x^{2} \sqrt{3 x} + \sqrt{{(x^{2})}^{2} \cdot 3 x}$

Add parentheses.

$- 40 x^{2} \sqrt{3 x} + \sqrt{{(x^{2})}^{2} \cdot (3 x)}$

Pull terms out from under the radical.

$- 40 x^{2} \sqrt{3 x} + x^{2} \sqrt{3 x}$

Add $- 40 x^{2} \sqrt{3 x}$ and $x^{2} \sqrt{3 x}$ .

$- 39 x^{2} \sqrt{3 x}$