Trigonometry Examples

$\sqrt{2} (\sqrt{15} - 4 \sqrt{2})$

Step 1

Apply the distributive property.

$\sqrt{2} \sqrt{15} + \sqrt{2} (- 4 \sqrt{2})$

Step 2

Combine using the product rule for radicals.

$\sqrt{2 \cdot 15} + \sqrt{2} (- 4 \sqrt{2})$

Step 3

Multiply $\sqrt{2} (- 4 \sqrt{2})$ .

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Step 3.1

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

$\sqrt{2 \cdot 15} - 4 ({\sqrt{2}}^{1} \sqrt{2})$

Step 3.2

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

$\sqrt{2 \cdot 15} - 4 ({\sqrt{2}}^{1} {\sqrt{2}}^{1})$

Step 3.3

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

$\sqrt{2 \cdot 15} - 4 {\sqrt{2}}^{1 + 1}$

Step 3.4

Add $1$ and $1$ .

$\sqrt{2 \cdot 15} - 4 {\sqrt{2}}^{2}$

Step 4

Simplify each term.

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Step 4.1

Multiply $2$ by $15$ .

$\sqrt{30} - 4 {\sqrt{2}}^{2}$

Step 4.2

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

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Step 4.2.1

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

$\sqrt{30} - 4 {(2^{\frac{1}{2}})}^{2}$

Step 4.2.2

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

$\sqrt{30} - 4 \cdot 2^{\frac{1}{2} \cdot 2}$

Step 4.2.3

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

$\sqrt{30} - 4 \cdot 2^{\frac{2}{2}}$

Step 4.2.4

Cancel the common factor of $2$ .

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Step 4.2.4.1

Cancel the common factor.

$\sqrt{30} - 4 \cdot 2^{\frac{2}{2}}$

Step 4.2.4.2

Rewrite the expression.

$\sqrt{30} - 4 \cdot 2^{1}$

Step 4.2.5

Evaluate the exponent.

$\sqrt{30} - 4 \cdot 2$

Step 4.3

Multiply $- 4$ by $2$ .

$\sqrt{30} - 8$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\sqrt{30} - 8$

Decimal Form:

$- 2.52277442 \dots$