Trigonometry Examples

$\sqrt{\frac{\frac{13}{13} - \frac{5}{13}}{2}}$

Step 1

Combine the numerators over the common denominator.

$\sqrt{\frac{\frac{13 - 5}{13}}{2}}$

Step 2

Subtract $5$ from $13$ .

$\sqrt{\frac{\frac{8}{13}}{2}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\sqrt{\frac{8}{13} \cdot \frac{1}{2}}$

Step 4

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.1

Factor $2$ out of $8$ .

$\sqrt{\frac{2 (4)}{13} \cdot \frac{1}{2}}$

Step 4.2

Cancel the common factor.

$\sqrt{\frac{2 \cdot 4}{13} \cdot \frac{1}{2}}$

Step 4.3

Rewrite the expression.

$\sqrt{\frac{4}{13}}$

Step 5

Rewrite $\sqrt{\frac{4}{13}}$ as $\frac{\sqrt{4}}{\sqrt{13}}$ .

$\frac{\sqrt{4}}{\sqrt{13}}$

Step 6

Simplify the numerator.

Tap for more steps...

Step 6.1

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

$\frac{\sqrt{2^{2}}}{\sqrt{13}}$

Step 6.2

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

$\frac{2}{\sqrt{13}}$

Step 7

Multiply $\frac{2}{\sqrt{13}}$ by $\frac{\sqrt{13}}{\sqrt{13}}$ .

$\frac{2}{\sqrt{13}} \cdot \frac{\sqrt{13}}{\sqrt{13}}$

Step 8

Combine and simplify the denominator.

Tap for more steps...

Step 8.1

Multiply $\frac{2}{\sqrt{13}}$ by $\frac{\sqrt{13}}{\sqrt{13}}$ .

$\frac{2 \sqrt{13}}{\sqrt{13} \sqrt{13}}$

Step 8.2

Raise $\sqrt{13}$ to the power of $1$ .

$\frac{2 \sqrt{13}}{{\sqrt{13}}^{1} \sqrt{13}}$

Step 8.3

Raise $\sqrt{13}$ to the power of $1$ .

$\frac{2 \sqrt{13}}{{\sqrt{13}}^{1} {\sqrt{13}}^{1}}$

Step 8.4

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

$\frac{2 \sqrt{13}}{{\sqrt{13}}^{1 + 1}}$

Step 8.5

Add $1$ and $1$ .

$\frac{2 \sqrt{13}}{{\sqrt{13}}^{2}}$

Step 8.6

Rewrite ${\sqrt{13}}^{2}$ as $13$ .

Tap for more steps...

Step 8.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{13}$ as $13^{\frac{1}{2}}$ .

$\frac{2 \sqrt{13}}{{(13^{\frac{1}{2}})}^{2}}$

Step 8.6.2

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

$\frac{2 \sqrt{13}}{13^{\frac{1}{2} \cdot 2}}$

Step 8.6.3

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

$\frac{2 \sqrt{13}}{13^{\frac{2}{2}}}$

Step 8.6.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 8.6.4.1

Cancel the common factor.

$\frac{2 \sqrt{13}}{13^{\frac{2}{2}}}$

Step 8.6.4.2

Rewrite the expression.

$\frac{2 \sqrt{13}}{13^{1}}$

Step 8.6.5

Evaluate the exponent.

$\frac{2 \sqrt{13}}{13}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{2 \sqrt{13}}{13}$

Decimal Form:

$0.55470019 \dots$