Trigonometry Examples

$6 \sqrt{18 x} - 4 \sqrt{8 x}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $9$ out of $18$ .

$6 \sqrt{9 (2) x} - 4 \sqrt{8 x}$

Step 1.1.2

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

$6 \sqrt{3^{2} \cdot 2 x} - 4 \sqrt{8 x}$

Step 1.1.3

Add parentheses.

$6 \sqrt{3^{2} \cdot (2 x)} - 4 \sqrt{8 x}$

$6 \sqrt{3^{2} \cdot (2 x)} - 4 \sqrt{8 x}$

Step 1.2

Pull terms out from under the radical.

$6 (3 \sqrt{2 x}) - 4 \sqrt{8 x}$

Step 1.3

Multiply $3$ by $6$ .

$18 \sqrt{2 x} - 4 \sqrt{8 x}$

Step 1.4

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

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Step 1.4.1

Factor $4$ out of $8$ .

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

Step 1.4.2

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

$18 \sqrt{2 x} - 4 \sqrt{2^{2} \cdot 2 x}$

Step 1.4.3

Add parentheses.

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

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

Step 1.5

Pull terms out from under the radical.

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

Step 1.6

Multiply $2$ by $- 4$ .

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

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

Step 2

Subtract $8 \sqrt{2 x}$ from $18 \sqrt{2 x}$ .

$10 \sqrt{2 x}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$