Evaluate square root of (1-(-6/( square root of 6)))/2

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Trigonometry

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

Multiply $\frac{6}{\sqrt{6}}$ by $\frac{\sqrt{6}}{\sqrt{6}}$ .

$\sqrt{\frac{1 - - (\frac{6}{\sqrt{6}} \cdot \frac{\sqrt{6}}{\sqrt{6}})}{2}}$

Combine and simplify the denominator.

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Multiply $\frac{6}{\sqrt{6}}$ and $\frac{\sqrt{6}}{\sqrt{6}}$ .

$\sqrt{\frac{1 - - \frac{6 \sqrt{6}}{\sqrt{6} \sqrt{6}}}{2}}$

Raise $\sqrt{6}$ to the power of $1$ .

$\sqrt{\frac{1 - - \frac{6 \sqrt{6}}{{\sqrt{6}}^{1} \sqrt{6}}}{2}}$

Raise $\sqrt{6}$ to the power of $1$ .

$\sqrt{\frac{1 - - \frac{6 \sqrt{6}}{{\sqrt{6}}^{1} {\sqrt{6}}^{1}}}{2}}$

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

$\sqrt{\frac{1 - - \frac{6 \sqrt{6}}{{\sqrt{6}}^{1 + 1}}}{2}}$

Add $1$ and $1$ .

$\sqrt{\frac{1 - - \frac{6 \sqrt{6}}{{\sqrt{6}}^{2}}}{2}}$

Rewrite ${\sqrt{6}}^{2}$ as $6$ .

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Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6}$ as $6^{\frac{1}{2}}$ .

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

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

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

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

$\sqrt{\frac{1 - - \frac{6 \sqrt{6}}{6^{\frac{2}{2}}}}{2}}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\sqrt{\frac{1 - - \frac{6 \sqrt{6}}{6^{\frac{2}{2}}}}{2}}$

Divide $1$ by $1$ .

$\sqrt{\frac{1 - - \frac{6 \sqrt{6}}{6^{1}}}{2}}$

Evaluate the exponent.

$\sqrt{\frac{1 - - \frac{6 \sqrt{6}}{6}}{2}}$

Cancel the common factor of $6$ .

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Cancel the common factor.

$\sqrt{\frac{1 - - \frac{6 \sqrt{6}}{6}}{2}}$

Divide $\sqrt{6}$ by $1$ .

$\sqrt{\frac{1 - - \sqrt{6}}{2}}$

Multiply $- - \sqrt{6}$ .

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Multiply $- 1$ by $- 1$ .

$\sqrt{\frac{1 + 1 \sqrt{6}}{2}}$

Multiply $\sqrt{6}$ by $1$ .

$\sqrt{\frac{1 + \sqrt{6}}{2}}$

Rewrite $\sqrt{\frac{1 + \sqrt{6}}{2}}$ as $\frac{\sqrt{1 + \sqrt{6}}}{\sqrt{2}}$ .

$\frac{\sqrt{1 + \sqrt{6}}}{\sqrt{2}}$

Multiply $\frac{\sqrt{1 + \sqrt{6}}}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{\sqrt{1 + \sqrt{6}}}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}$

Combine and simplify the denominator.

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Multiply $\frac{\sqrt{1 + \sqrt{6}}}{\sqrt{2}}$ and $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{\sqrt{1 + \sqrt{6}} \sqrt{2}}{\sqrt{2} \sqrt{2}}$

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

$\frac{\sqrt{1 + \sqrt{6}} \sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}}$

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

$\frac{\sqrt{1 + \sqrt{6}} \sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}}$

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

$\frac{\sqrt{1 + \sqrt{6}} \sqrt{2}}{{\sqrt{2}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{\sqrt{1 + \sqrt{6}} \sqrt{2}}{{\sqrt{2}}^{2}}$

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

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

$\frac{\sqrt{1 + \sqrt{6}} \sqrt{2}}{{(2^{\frac{1}{2}})}^{2}}$

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

$\frac{\sqrt{1 + \sqrt{6}} \sqrt{2}}{2^{\frac{1}{2} \cdot 2}}$

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

$\frac{\sqrt{1 + \sqrt{6}} \sqrt{2}}{2^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{\sqrt{1 + \sqrt{6}} \sqrt{2}}{2^{\frac{2}{2}}}$

Divide $1$ by $1$ .

$\frac{\sqrt{1 + \sqrt{6}} \sqrt{2}}{2^{1}}$

Evaluate the exponent.

$\frac{\sqrt{1 + \sqrt{6}} \sqrt{2}}{2}$

Combine using the product rule for radicals.

$\frac{\sqrt{(1 + \sqrt{6}) \cdot 2}}{2}$

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{(1 + \sqrt{6}) \cdot 2}}{2}$

Decimal Form:

$1.31329542 \dots$

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Name

Name	eight hundred three million one hundred forty-six thousand one hundred sixty-six

Interesting facts

803146166 has 8 divisors, whose sum is 1205446080
The reverse of 803146166 is 661641308
Previous prime number is 1669

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 35
Digital Root 8

Name

Name	four hundred sixty-seven million seven hundred sixty-six thousand three hundred eighty-seven

Interesting facts

467766387 has 32 divisors, whose sum is 788866560
The reverse of 467766387 is 783667764
Previous prime number is 11

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 54
Digital Root 9

Name

Name	one billion one hundred sixty-seven million four hundred eighty-seven thousand one hundred thirty-eight

Interesting facts

1167487138 has 8 divisors, whose sum is 1854244332
The reverse of 1167487138 is 8317847611
Previous prime number is 17

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 46
Digital Root 1

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