Simplify square root of 8x^2+2x square root of 2- square root of 20x

$\sqrt{8 x^{2}} + 2 x \sqrt{2} - \sqrt{20 x}$

Simplify each term.

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

Factor $4$ out of $8$ .

$\sqrt{4 (2) x^{2}} + 2 x \sqrt{2} - \sqrt{20 x}$

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

$\sqrt{2^{2} \cdot 2 x^{2}} + 2 x \sqrt{2} - \sqrt{20 x}$

Move $2$ .

$\sqrt{2^{2} x^{2} \cdot 2} + 2 x \sqrt{2} - \sqrt{20 x}$

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

$\sqrt{{(2 x)}^{2} \cdot 2} + 2 x \sqrt{2} - \sqrt{20 x}$

Pull terms out from under the radical.

$2 x \sqrt{2} + 2 x \sqrt{2} - \sqrt{20 x}$

Rewrite $20 x$ as $2^{2} \cdot (5 x)$ .

Factor $4$ out of $20$ .

$2 x \sqrt{2} + 2 x \sqrt{2} - \sqrt{4 (5) x}$

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Multiply $2$ by $- 1$ .

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

Add $2 x \sqrt{2}$ and $2 x \sqrt{2}$ .

$4 x \sqrt{2} - 2 \sqrt{5 x}$