Trigonometry Examples

$2 \sqrt{2} (- 3 \sqrt{2}) - 2 \sqrt{2} \frac{1}{2}$

Step 1

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

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Step 1.1

Multiply $- 3$ by $2$ .

$- 6 \sqrt{2} \sqrt{2} - 2 \sqrt{2} \frac{1}{2}$

Step 1.2

Raise $\sqrt{2}$ to the power of $1$ .

$- 6 ({\sqrt{2}}^{1} \sqrt{2}) - 2 \sqrt{2} \frac{1}{2}$

Step 1.3

Raise $\sqrt{2}$ to the power of $1$ .

$- 6 ({\sqrt{2}}^{1} {\sqrt{2}}^{1}) - 2 \sqrt{2} \frac{1}{2}$

Step 1.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 6 {\sqrt{2}}^{1 + 1} - 2 \sqrt{2} \frac{1}{2}$

Step 1.5

Add $1$ and $1$ .

$- 6 {\sqrt{2}}^{2} - 2 \sqrt{2} \frac{1}{2}$

Step 2

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

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Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$- 6 {(2^{\frac{1}{2}})}^{2} - 2 \sqrt{2} \frac{1}{2}$

Step 2.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- 6 \cdot 2^{\frac{1}{2} \cdot 2} - 2 \sqrt{2} \frac{1}{2}$

Step 2.3

Combine $\frac{1}{2}$ and $2$ .

$- 6 \cdot 2^{\frac{2}{2}} - 2 \sqrt{2} \frac{1}{2}$

Step 2.4

Cancel the common factor of $2$ .

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Step 2.4.1

Cancel the common factor.

$- 6 \cdot 2^{\frac{2}{2}} - 2 \sqrt{2} \frac{1}{2}$

Step 2.4.2

Rewrite the expression.

$- 6 \cdot 2^{1} - 2 \sqrt{2} \frac{1}{2}$

Step 2.5

Evaluate the exponent.

$- 6 \cdot 2 - 2 \sqrt{2} \frac{1}{2}$

Step 3

Multiply $- 6$ by $2$ .

$- 12 - 2 \sqrt{2} \frac{1}{2}$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Factor $2$ out of $- 2 \sqrt{2}$ .

$- 12 + 2 (- \sqrt{2}) \frac{1}{2}$

Step 4.2

Cancel the common factor.

$- 12 + 2 (- \sqrt{2}) \frac{1}{2}$

Step 4.3

Rewrite the expression.

$- 12 - \sqrt{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- 12 - \sqrt{2}$

Decimal Form:

$- 13.41421356 \dots$