What is the value of arccos((57)/(sqrt(129*\sqrt{53))}) ?

The value of arccos((57)/(sqrt(129*\sqrt{53))}) is No Solution for x\in\mathbb{R}

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arccos((57)/(sqrt(129*\sqrt{53))})

Solution

arccos (\frac{57}{129 \cdot 53})

Solution

No Solution for x \in R

Solution steps

arccos (\frac{57}{129 53})

Simplify:

\frac{57}{129 53} = \frac{19 129 \cdot 5 3 ^{\frac{3}{4}}}{2279}

\frac{57}{129 53}

Factor

57 : 3 \cdot 19

Factor

57 = 3 \cdot 19

Factor

12953 : 34353

Factor

129 = 3 \cdot 43

= 3 \cdot 4353

Apply radical rule:

= 34353

= \frac{3 \cdot 19}{3 43 53}

Cancel

\frac{3 \cdot 19}{3 43 53} : \frac{3 \cdot 19}{43 53}

\frac{3 \cdot 19}{3 43 53}

Apply radical rule:

3 = 3^{\frac{1}{2}}

= \frac{3 \cdot 19}{3 ^{\frac{1}{2}} 43 53}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{3 ^{1}}{3 ^{\frac{1}{2}}} = 3^{1 - \frac{1}{2}}

= \frac{19 \cdot 3 ^{- \frac{1}{2} + 1}}{43 53}

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{19 \cdot 3 ^{\frac{1}{2}}}{43 53}

Apply radical rule:

3^{\frac{1}{2}} = 3

= \frac{19 3}{43 53}

= \frac{3 \cdot 19}{43 53}

Simplify

53

Apply radical rule:

a = a^{\frac{1}{2}}

= (5 3^{\frac{1}{2}})^{\frac{1}{2}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= 5 3^{\frac{1}{2} \cdot \frac{1}{2}}

\frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4}

\frac{1}{2} \cdot \frac{1}{2}

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot 1}{2 \cdot 2}

Multiply the numbers:

1 \cdot 1 = 1

= \frac{1}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{1}{4}

= 5 3^{\frac{1}{4}}

Rationalize

Multiply by the conjugate

\frac{43}{43}

3 \cdot 1943 = 19129

3 \cdot 1943

Apply radical rule:

a b = a \cdot b

343 = 3 \cdot 43

= 19 3 \cdot 43

Multiply the numbers:

3 \cdot 43 = 129

= 19129

Apply radical rule:

a a = a

4343 = 43

Multiply by the conjugate

\frac{5 3 ^{\frac{3}{4}}}{5 3 ^{\frac{3}{4}}}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

= 43 \cdot 5 3^{\frac{3}{4} + \frac{1}{4}}

5 3^{\frac{3}{4} + \frac{1}{4}} = 53

5 3^{\frac{3}{4} + \frac{1}{4}}

Combine the fractions

\frac{3}{4} + \frac{1}{4} : 1

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{3 + 1}{4}

Add the numbers:

3 + 1 = 4

= \frac{4}{4}

Apply rule

\frac{a}{a} = 1

= 1

= 5 3^{1}

Apply rule

a^{1} = a

= 53

= 43 \cdot 53

Multiply the numbers:

43 \cdot 53 = 2279

= 2279

= \frac{19 129 \cdot 5 3 ^{\frac{3}{4}}}{2279}

= \frac{19 129 \cdot 5 3 ^{\frac{3}{4}}}{2279}

= arccos (\frac{19 129 \cdot 5 3 ^{\frac{3}{4}}}{2279})

Real domain for

arccos (x)

- 1 \leq x \leq 1

No Solution for x \in R

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Frequently Asked Questions (FAQ)

What is the value of arccos((57)/(sqrt(129*\sqrt{53))}) ?
The value of arccos((57)/(sqrt(129*\sqrt{53))}) is No Solution for x\in\mathbb{R}