What is sqrt(((5)^2-(12)^2)^{-1)} ?

The solution to sqrt(((5)^2-(12)^2)^{-1)} is -i(sqrt(119))/(119)

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simplify sqrt(((5)^2-(12)^2)^{-1)}

simplify

((5)^{2} - (12)^{2})^{- 1}

- i \frac{119}{119}

Solution steps

((5)^{2} - (12)^{2})^{- 1}

Apply radical rule:

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

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

Apply exponent rule:

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

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

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

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

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{5 ^{2} - 1 2 ^{2}}

Apply imaginary number rule:

- a = i a

= \frac{1}{i 1 2 ^{2} - 5 ^{2}}

- 5^{2} + 1 2^{2} = 119

= \frac{1}{119 i}

Rationalize

\frac{1}{119 i} : - \frac{i}{119}

= - \frac{i}{119}

Rewrite

- \frac{i}{119}

in standard complex form:

- \frac{119}{119} i

= - \frac{119}{119} i

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What is sqrt(((5)^2-(12)^2)^{-1)} ?
The solution to sqrt(((5)^2-(12)^2)^{-1)} is -i(sqrt(119))/(119)