Trigonometry Examples

$\sqrt{2} (\sqrt{18} - \sqrt{8})$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $9$ out of $18$ .

$\sqrt{2} (\sqrt{9 (2)} - \sqrt{8})$

Step 1.1.2

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

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

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

Step 1.2

Pull terms out from under the radical.

$\sqrt{2} (3 \sqrt{2} - \sqrt{8})$

Step 1.3

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 1.3.1

Factor $4$ out of $8$ .

$\sqrt{2} (3 \sqrt{2} - \sqrt{4 (2)})$

Step 1.3.2

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

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

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

Step 1.4

Pull terms out from under the radical.

$\sqrt{2} (3 \sqrt{2} - (2 \sqrt{2}))$

Step 1.5

Multiply $2$ by $- 1$ .

$\sqrt{2} (3 \sqrt{2} - 2 \sqrt{2})$

$\sqrt{2} (3 \sqrt{2} - 2 \sqrt{2})$

Step 2

Simplify terms.

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Step 2.1

Subtract $2 \sqrt{2}$ from $3 \sqrt{2}$ .

$\sqrt{2} \sqrt{2}$

Step 2.2

Combine using the product rule for radicals.

$\sqrt{2 \cdot 2}$

Step 2.3

Write the expression using exponents.

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Step 2.3.1

Multiply $2$ by $2$ .

$\sqrt{4}$

Step 2.3.2

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

$\sqrt{2^{2}}$

$\sqrt{2^{2}}$

$\sqrt{2^{2}}$

Step 3

Pull terms out from under the radical, assuming positive real numbers.

$2$

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