Simplify arcsin( square root of 3/2)

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Trigonometry

$\arcsin (\sqrt{\frac{3}{2}})$

Rewrite $\sqrt{\frac{3}{2}}$ as $\frac{\sqrt{3}}{\sqrt{2}}$ .

$\arcsin (\frac{\sqrt{3}}{\sqrt{2}})$

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

$\arcsin (\frac{\sqrt{3}}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}})$

Combine and simplify the denominator.

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Multiply $\frac{\sqrt{3}}{\sqrt{2}}$ and $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\arcsin (\frac{\sqrt{3} \sqrt{2}}{\sqrt{2} \sqrt{2}})$

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

$\arcsin (\frac{\sqrt{3} \sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}})$

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

$\arcsin (\frac{\sqrt{3} \sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}})$

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

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

Add $1$ and $1$ .

$\arcsin (\frac{\sqrt{3} \sqrt{2}}{{\sqrt{2}}^{2}})$

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

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Rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$\arcsin (\frac{\sqrt{3} \sqrt{2}}{{(2^{\frac{1}{2}})}^{2}})$

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

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

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

$\arcsin (\frac{\sqrt{3} \sqrt{2}}{2^{\frac{2}{2}}})$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\arcsin (\frac{\sqrt{3} \sqrt{2}}{2^{\frac{2}{2}}})$

Divide $1$ by $1$ .

$\arcsin (\frac{\sqrt{3} \sqrt{2}}{2^{1}})$

Evaluate the exponent.

$\arcsin (\frac{\sqrt{3} \sqrt{2}}{2})$

Simplify the numerator.

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Combine using the product rule for radicals.

$\arcsin (\frac{\sqrt{3 \cdot 2}}{2})$

Multiply $3$ by $2$ .

$\arcsin (\frac{\sqrt{6}}{2})$

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Name

Name	one billion one hundred nine million five hundred thirty-seven thousand two hundred eighteen

Interesting facts

1109537218 has 8 divisors, whose sum is 1680464448
The reverse of 1109537218 is 8127359011
Previous prime number is 103

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 37
Digital Root 1

Name

Name	six hundred thirteen million four hundred ninety-two thousand five hundred thirty-three

Interesting facts

613492533 has 8 divisors, whose sum is 1090653408
The reverse of 613492533 is 335294316
Previous prime number is 3

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 36
Digital Root 9

Name

Name	one billion three hundred ten million one hundred seventeen thousand thirty-eight

Interesting facts

1310117038 has 4 divisors, whose sum is 1965175560
The reverse of 1310117038 is 8307110131
Previous prime number is 2

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 25
Digital Root 7

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