Trigonometry Examples

$\sqrt{3} (6 \sqrt{3} - \sqrt{14})$

Step 1

Apply the distributive property.

$\sqrt{3} (6 \sqrt{3}) + \sqrt{3} (- \sqrt{14})$

Step 2

Multiply $\sqrt{3} (6 \sqrt{3})$ .

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Step 2.1

Raise $\sqrt{3}$ to the power of $1$ .

$6 ({\sqrt{3}}^{1} \sqrt{3}) + \sqrt{3} (- \sqrt{14})$

Step 2.2

Raise $\sqrt{3}$ to the power of $1$ .

$6 ({\sqrt{3}}^{1} {\sqrt{3}}^{1}) + \sqrt{3} (- \sqrt{14})$

Step 2.3

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

$6 {\sqrt{3}}^{1 + 1} + \sqrt{3} (- \sqrt{14})$

Step 2.4

Add $1$ and $1$ .

$6 {\sqrt{3}}^{2} + \sqrt{3} (- \sqrt{14})$

Step 3

Multiply $\sqrt{3} (- \sqrt{14})$ .

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Step 3.1

Combine using the product rule for radicals.

$6 {\sqrt{3}}^{2} - \sqrt{3 \cdot 14}$

Step 3.2

Multiply $3$ by $14$ .

$6 {\sqrt{3}}^{2} - \sqrt{42}$

Step 4

Simplify each term.

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Step 4.1

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Step 4.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$6 {(3^{\frac{1}{2}})}^{2} - \sqrt{42}$

Step 4.1.2

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

$6 \cdot 3^{\frac{1}{2} \cdot 2} - \sqrt{42}$

Step 4.1.3

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

$6 \cdot 3^{\frac{2}{2}} - \sqrt{42}$

Step 4.1.4

Cancel the common factor of $2$ .

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Step 4.1.4.1

Cancel the common factor.

$6 \cdot 3^{\frac{2}{2}} - \sqrt{42}$

Step 4.1.4.2

Rewrite the expression.

$6 \cdot 3^{1} - \sqrt{42}$

Step 4.1.5

Evaluate the exponent.

$6 \cdot 3 - \sqrt{42}$

Step 4.2

Multiply $6$ by $3$ .

$18 - \sqrt{42}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$18 - \sqrt{42}$

Decimal Form:

$11.51925930 \dots$