Trigonometry Examples

$2 (\frac{\sqrt{5}}{5}) (\frac{2 \sqrt{5}}{5})$

Step 1

Combine $2$ and $\frac{\sqrt{5}}{5}$ .

$\frac{2 \sqrt{5}}{5} \cdot \frac{2 \sqrt{5}}{5}$

Step 2

Multiply $\frac{2 \sqrt{5}}{5} \cdot \frac{2 \sqrt{5}}{5}$ .

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Step 2.1

Multiply $\frac{2 \sqrt{5}}{5}$ by $\frac{2 \sqrt{5}}{5}$ .

$\frac{2 \sqrt{5} (2 \sqrt{5})}{5 \cdot 5}$

Step 2.2

Multiply $2$ by $2$ .

$\frac{4 \sqrt{5} \sqrt{5}}{5 \cdot 5}$

Step 2.3

Raise $\sqrt{5}$ to the power of $1$ .

$\frac{4 ({\sqrt{5}}^{1} \sqrt{5})}{5 \cdot 5}$

Step 2.4

Raise $\sqrt{5}$ to the power of $1$ .

$\frac{4 ({\sqrt{5}}^{1} {\sqrt{5}}^{1})}{5 \cdot 5}$

Step 2.5

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

$\frac{4 {\sqrt{5}}^{1 + 1}}{5 \cdot 5}$

Step 2.6

Add $1$ and $1$ .

$\frac{4 {\sqrt{5}}^{2}}{5 \cdot 5}$

Step 2.7

Multiply $5$ by $5$ .

$\frac{4 {\sqrt{5}}^{2}}{25}$

Step 3

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

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Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$\frac{4 {(5^{\frac{1}{2}})}^{2}}{25}$

Step 3.2

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

$\frac{4 \cdot 5^{\frac{1}{2} \cdot 2}}{25}$

Step 3.3

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

$\frac{4 \cdot 5^{\frac{2}{2}}}{25}$

Step 3.4

Cancel the common factor of $2$ .

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Step 3.4.1

Cancel the common factor.

$\frac{4 \cdot 5^{\frac{2}{2}}}{25}$

Step 3.4.2

Rewrite the expression.

$\frac{4 \cdot 5^{1}}{25}$

Step 3.5

Evaluate the exponent.

$\frac{4 \cdot 5}{25}$

Step 4

Multiply $4$ by $5$ .

$\frac{20}{25}$

Step 5

Cancel the common factor of $20$ and $25$ .

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Step 5.1

Factor $5$ out of $20$ .

$\frac{5 (4)}{25}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $5$ out of $25$ .

$\frac{5 \cdot 4}{5 \cdot 5}$

Step 5.2.2

Cancel the common factor.

$\frac{5 \cdot 4}{5 \cdot 5}$

Step 5.2.3

Rewrite the expression.

$\frac{4}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{5}$

Decimal Form:

$0.8$