Simplify the Radical Expression square root of 2x- square root of 8x^3+3 square root of 18x

$\sqrt{2 x} - \sqrt{8 x^{3}} + 3 \sqrt{18 x}$

Step 1

Simplify each term.

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

Factor $4$ out of $8$ .

$\sqrt{2 x} - \sqrt{4 (2) x^{3}} + 3 \sqrt{18 x}$

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

$\sqrt{2 x} - \sqrt{2^{2} \cdot 2 x^{3}} + 3 \sqrt{18 x}$

Factor out $x^{2}$ .

$\sqrt{2 x} - \sqrt{2^{2} \cdot 2 (x^{2} x)} + 3 \sqrt{18 x}$

Move $2$ .

$\sqrt{2 x} - \sqrt{2^{2} x^{2} \cdot 2 x} + 3 \sqrt{18 x}$

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

$\sqrt{2 x} - \sqrt{{(2 x)}^{2} \cdot 2 x} + 3 \sqrt{18 x}$

Add parentheses.

$\sqrt{2 x} - \sqrt{{(2 x)}^{2} \cdot (2 x)} + 3 \sqrt{18 x}$

Pull terms out from under the radical.

$\sqrt{2 x} - (| 2 x | \sqrt{2 x}) + 3 \sqrt{18 x}$

Remove non-negative terms from the absolute value.

$\sqrt{2 x} - (2 | x | \sqrt{2 x}) + 3 \sqrt{18 x}$

Multiply $2$ by $- 1$ .

$\sqrt{2 x} - 2 (| x | \sqrt{2 x}) + 3 \sqrt{18 x}$

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

Factor $9$ out of $18$ .

$\sqrt{2 x} - 2 | x | \sqrt{2 x} + 3 \sqrt{9 (2) x}$

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

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

Multiply $3$ by $3$ .

$\sqrt{2 x} - 2 | x | \sqrt{2 x} + 9 \sqrt{2 x}$

Step 2

Add $\sqrt{2 x}$ and $9 \sqrt{2 x}$ .

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