Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $4$ out of $8$ .

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

Step 1.1.2

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

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

Step 1.1.3

Factor out $x^{2}$ .

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

Step 1.1.4

Move $2$ .

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

Step 1.1.5

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

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

Step 1.1.6

Add parentheses.

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

Step 1.2

Pull terms out from under the radical.

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

Step 1.3

Remove non-negative terms from the absolute value.

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

Step 1.4

Multiply $2$ by $- 1$ .

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

Step 1.5

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

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Step 1.5.1

Factor $9$ out of $18$ .

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

Step 1.5.2

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

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

Step 1.5.3

Add parentheses.

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

Step 1.6

Pull terms out from under the radical.

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

Step 1.7

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

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

Step 1.8

Multiply $3$ by $3$ .

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

Step 2

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

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