Simplify square root of 2x- square root of 8x^3-4 square root of 8x^3

$\sqrt{2 x} - \sqrt{8 x^{3}} - 4 \sqrt{8 x^{3}}$

Simplify each term.

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

Factor $4$ out of $8$ .

$\sqrt{2 x} - \sqrt{4 (2) x^{3}} - 4 \sqrt{8 x^{3}}$

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

$\sqrt{2 x} - \sqrt{2^{2} \cdot 2 x^{3}} - 4 \sqrt{8 x^{3}}$

Factor out $x^{2}$ .

$\sqrt{2 x} - \sqrt{2^{2} \cdot 2 (x^{2} x)} - 4 \sqrt{8 x^{3}}$

Move $2$ .

$\sqrt{2 x} - \sqrt{2^{2} x^{2} \cdot 2 x} - 4 \sqrt{8 x^{3}}$

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

$\sqrt{2 x} - \sqrt{{(2 x)}^{2} \cdot 2 x} - 4 \sqrt{8 x^{3}}$

Add parentheses.

$\sqrt{2 x} - \sqrt{{(2 x)}^{2} \cdot (2 x)} - 4 \sqrt{8 x^{3}}$

Pull terms out from under the radical.

$\sqrt{2 x} - (2 x \sqrt{2 x}) - 4 \sqrt{8 x^{3}}$

Multiply $2$ by $- 1$ .

$\sqrt{2 x} - 2 (x \sqrt{2 x}) - 4 \sqrt{8 x^{3}}$

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

Factor $4$ out of $8$ .

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

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

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

Factor out $x^{2}$ .

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

Move $2$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

$\sqrt{2 x} - 2 x \sqrt{2 x} - 4 (2 x \sqrt{2 x})$

Multiply $2$ by $- 4$ .

$\sqrt{2 x} - 2 x \sqrt{2 x} - 8 x \sqrt{2 x}$

Subtract $8 x \sqrt{2 x}$ from $- 2 x \sqrt{2 x}$ .

$\sqrt{2 x} - 10 x \sqrt{2 x}$