Trigonometry Examples

$\sqrt{1 - \frac{- \frac{3}{\sqrt{73}}}{2}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\sqrt{1 - (- \frac{3}{\sqrt{73}} \cdot \frac{1}{2})}$

Step 2

Multiply $\frac{3}{\sqrt{73}}$ by $\frac{\sqrt{73}}{\sqrt{73}}$ .

$\sqrt{1 - (- (\frac{3}{\sqrt{73}} \cdot \frac{\sqrt{73}}{\sqrt{73}}) \frac{1}{2})}$

Step 3

Combine and simplify the denominator.

Tap for more steps...

Step 3.1

Multiply $\frac{3}{\sqrt{73}}$ by $\frac{\sqrt{73}}{\sqrt{73}}$ .

$\sqrt{1 - (- \frac{3 \sqrt{73}}{\sqrt{73} \sqrt{73}} \cdot \frac{1}{2})}$

Step 3.2

Raise $\sqrt{73}$ to the power of $1$ .

$\sqrt{1 - (- \frac{3 \sqrt{73}}{{\sqrt{73}}^{1} \sqrt{73}} \cdot \frac{1}{2})}$

Step 3.3

Raise $\sqrt{73}$ to the power of $1$ .

$\sqrt{1 - (- \frac{3 \sqrt{73}}{{\sqrt{73}}^{1} {\sqrt{73}}^{1}} \cdot \frac{1}{2})}$

Step 3.4

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

$\sqrt{1 - (- \frac{3 \sqrt{73}}{{\sqrt{73}}^{1 + 1}} \cdot \frac{1}{2})}$

Step 3.5

Add $1$ and $1$ .

$\sqrt{1 - (- \frac{3 \sqrt{73}}{{\sqrt{73}}^{2}} \cdot \frac{1}{2})}$

Step 3.6

Rewrite ${\sqrt{73}}^{2}$ as $73$ .

Tap for more steps...

Step 3.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{73}$ as $73^{\frac{1}{2}}$ .

$\sqrt{1 - (- \frac{3 \sqrt{73}}{{(73^{\frac{1}{2}})}^{2}} \cdot \frac{1}{2})}$

Step 3.6.2

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

$\sqrt{1 - (- \frac{3 \sqrt{73}}{73^{\frac{1}{2} \cdot 2}} \cdot \frac{1}{2})}$

Step 3.6.3

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

$\sqrt{1 - (- \frac{3 \sqrt{73}}{73^{\frac{2}{2}}} \cdot \frac{1}{2})}$

Step 3.6.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.6.4.1

Cancel the common factor.

$\sqrt{1 - (- \frac{3 \sqrt{73}}{73^{\frac{2}{2}}} \cdot \frac{1}{2})}$

Step 3.6.4.2

Rewrite the expression.

$\sqrt{1 - (- \frac{3 \sqrt{73}}{73^{1}} \cdot \frac{1}{2})}$

Step 3.6.5

Evaluate the exponent.

$\sqrt{1 - (- \frac{3 \sqrt{73}}{73} \cdot \frac{1}{2})}$

Step 4

Multiply $- \frac{3 \sqrt{73}}{73} \cdot \frac{1}{2}$ .

Tap for more steps...

Step 4.1

Multiply $\frac{1}{2}$ by $\frac{3 \sqrt{73}}{73}$ .

$\sqrt{1 - - \frac{3 \sqrt{73}}{2 \cdot 73}}$

Step 4.2

Multiply $2$ by $73$ .

$\sqrt{1 - - \frac{3 \sqrt{73}}{146}}$

Step 5

Multiply $- - \frac{3 \sqrt{73}}{146}$ .

Tap for more steps...

Step 5.1

Multiply $- 1$ by $- 1$ .

$\sqrt{1 + 1 \frac{3 \sqrt{73}}{146}}$

Step 5.2

Multiply $\frac{3 \sqrt{73}}{146}$ by $1$ .

$\sqrt{1 + \frac{3 \sqrt{73}}{146}}$

Step 6

Write $1$ as a fraction with a common denominator.

$\sqrt{\frac{146}{146} + \frac{3 \sqrt{73}}{146}}$

Step 7

Combine the numerators over the common denominator.

$\sqrt{\frac{146 + 3 \sqrt{73}}{146}}$

Step 8

Rewrite $\sqrt{\frac{146 + 3 \sqrt{73}}{146}}$ as $\frac{\sqrt{146 + 3 \sqrt{73}}}{\sqrt{146}}$ .

$\frac{\sqrt{146 + 3 \sqrt{73}}}{\sqrt{146}}$

Step 9

Multiply $\frac{\sqrt{146 + 3 \sqrt{73}}}{\sqrt{146}}$ by $\frac{\sqrt{146}}{\sqrt{146}}$ .

$\frac{\sqrt{146 + 3 \sqrt{73}}}{\sqrt{146}} \cdot \frac{\sqrt{146}}{\sqrt{146}}$

Step 10

Combine and simplify the denominator.

Tap for more steps...

Step 10.1

Multiply $\frac{\sqrt{146 + 3 \sqrt{73}}}{\sqrt{146}}$ by $\frac{\sqrt{146}}{\sqrt{146}}$ .

$\frac{\sqrt{146 + 3 \sqrt{73}} \sqrt{146}}{\sqrt{146} \sqrt{146}}$

Step 10.2

Raise $\sqrt{146}$ to the power of $1$ .

$\frac{\sqrt{146 + 3 \sqrt{73}} \sqrt{146}}{{\sqrt{146}}^{1} \sqrt{146}}$

Step 10.3

Raise $\sqrt{146}$ to the power of $1$ .

$\frac{\sqrt{146 + 3 \sqrt{73}} \sqrt{146}}{{\sqrt{146}}^{1} {\sqrt{146}}^{1}}$

Step 10.4

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

$\frac{\sqrt{146 + 3 \sqrt{73}} \sqrt{146}}{{\sqrt{146}}^{1 + 1}}$

Step 10.5

Add $1$ and $1$ .

$\frac{\sqrt{146 + 3 \sqrt{73}} \sqrt{146}}{{\sqrt{146}}^{2}}$

Step 10.6

Rewrite ${\sqrt{146}}^{2}$ as $146$ .

Tap for more steps...

Step 10.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{146}$ as $146^{\frac{1}{2}}$ .

$\frac{\sqrt{146 + 3 \sqrt{73}} \sqrt{146}}{{(146^{\frac{1}{2}})}^{2}}$

Step 10.6.2

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

$\frac{\sqrt{146 + 3 \sqrt{73}} \sqrt{146}}{146^{\frac{1}{2} \cdot 2}}$

Step 10.6.3

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

$\frac{\sqrt{146 + 3 \sqrt{73}} \sqrt{146}}{146^{\frac{2}{2}}}$

Step 10.6.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 10.6.4.1

Cancel the common factor.

$\frac{\sqrt{146 + 3 \sqrt{73}} \sqrt{146}}{146^{\frac{2}{2}}}$

Step 10.6.4.2

Rewrite the expression.

$\frac{\sqrt{146 + 3 \sqrt{73}} \sqrt{146}}{146^{1}}$

Step 10.6.5

Evaluate the exponent.

$\frac{\sqrt{146 + 3 \sqrt{73}} \sqrt{146}}{146}$

Step 11

Combine using the product rule for radicals.

$\frac{\sqrt{(146 + 3 \sqrt{73}) \cdot 146}}{146}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{(146 + 3 \sqrt{73}) \cdot 146}}{146}$

Decimal Form:

$1.08423324 \dots$