Simplify square root of 2x- square root of 8x+ square root of 18x

$\sqrt{2 x} - \sqrt{8 x} + \sqrt{18 x}$

Step 1

Simplify each term.

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

Factor $4$ out of $8$ .

$\sqrt{2 x} - \sqrt{4 (2) x} + \sqrt{18 x}$

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

$\sqrt{2 x} - \sqrt{2^{2} \cdot 2 x} + \sqrt{18 x}$

Add parentheses.

$\sqrt{2 x} - \sqrt{2^{2} \cdot (2 x)} + \sqrt{18 x}$

Pull terms out from under the radical.

$\sqrt{2 x} - (2 \sqrt{2 x}) + \sqrt{18 x}$

Multiply $2$ by $- 1$ .

$\sqrt{2 x} - 2 \sqrt{2 x} + \sqrt{18 x}$

Rewrite $18 x$ as $3^{2} \cdot (2 x)$ .

Factor $9$ out of $18$ .

$\sqrt{2 x} - 2 \sqrt{2 x} + \sqrt{9 (2) x}$

Rewrite $9$ as $3^{2}$ .

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

Add parentheses.

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

Pull terms out from under the radical.

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

Step 2

Simplify by adding terms.

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

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

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

$2 \sqrt{2 x}$