What is the value of arccos((-58)/(sqrt(129\sqrt{53))}) ?

The value of arccos((-58)/(sqrt(129\sqrt{53))}) is No Solution for x\in\mathbb{R}

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arccos((-58)/(sqrt(129\sqrt{53))})

arccos (\frac{- 58}{129 53})

No Solution for x \in R

Solution steps

arccos (\frac{- 58}{129 53})

Simplify:

\frac{- 58}{129 53} = - \frac{58 129 \cdot 5 3 ^{\frac{3}{4}}}{6837}

\frac{- 58}{129 53}

Apply the fraction rule:

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

= - \frac{58}{129 53}

12953

Apply radical rule:

assuming

a \geq 0, b \geq 0

= 12953

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{129}{129}

Apply radical rule:

a a = a

129129 = 129

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}

= 129 \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

= 129 \cdot 53

Multiply the numbers:

129 \cdot 53 = 6837

= 6837

= - \frac{58 129 \cdot 5 3 ^{\frac{3}{4}}}{6837}

= - \frac{58 129 \cdot 5 3 ^{\frac{3}{4}}}{6837}

= arccos (- \frac{58 129 \cdot 5 3 ^{\frac{3}{4}}}{6837})

Real domain for

arccos (x)

- 1 \leq x \leq 1

No Solution for x \in R

arctan (\frac{21}{28})

cos^{2} (3 3^{\circ}) - sin^{2} (3 3^{\circ})

- 9 cos (- \frac{π}{6})

cos (π) + sin (π) i

tan (\frac{6 π}{6})

What is the value of arccos((-58)/(sqrt(129\sqrt{53))}) ?
The value of arccos((-58)/(sqrt(129\sqrt{53))}) is No Solution for x\in\mathbb{R}