Simplify square root of x^3+ square root of 16x^3-3x square root of x

$\sqrt{x^{3}} + \sqrt{16 x^{3}} - 3 x \sqrt{x}$

Simplify each term.

Factor out $x^{2}$ .

$\sqrt{x^{2} x} + \sqrt{16 x^{3}} - 3 x \sqrt{x}$

Pull terms out from under the radical.

$x \sqrt{x} + \sqrt{16 x^{3}} - 3 x \sqrt{x}$

Rewrite $16 x^{3}$ as ${(4 x)}^{2} x$ .

Rewrite $16$ as $4^{2}$ .

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

Factor out $x^{2}$ .

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

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

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

Pull terms out from under the radical.

$x \sqrt{x} + 4 x \sqrt{x} - 3 x \sqrt{x}$

Simplify by adding terms.

Add $x \sqrt{x}$ and $4 x \sqrt{x}$ .

$5 x \sqrt{x} - 3 x \sqrt{x}$

Subtract $3 x \sqrt{x}$ from $5 x \sqrt{x}$ .

$2 x \sqrt{x}$