What is sqrt((-125)/(216)) ?

The solution to sqrt((-125)/(216)) is i(5sqrt(30))/(36)

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simplify sqrt((-125)/(216))

simplify

\frac{- 125}{216}

i \frac{5 30}{36}

Solution steps

\frac{- 125}{216}

Apply the fraction rule:

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

= - \frac{125}{216}

Apply radical rule:

- a = - 1 a

- \frac{125}{216} = - 1 \frac{125}{216}

= - 1 \frac{125}{216}

Apply imaginary number rule:

- 1 = i

= i \frac{125}{216}

Apply radical rule:

assuming

a \geq 0, b \geq 0

\frac{125}{216} = \frac{125}{216}

= i \frac{125}{216}

216 = 66

= i \frac{125}{6 6}

125 = 55

= i \frac{5 5}{6 6}

Multiply fractions:

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

= \frac{5 5 i}{6 6}

Rationalize

\frac{5 5 i}{6 6} : \frac{5 30 i}{36}

= \frac{5 30 i}{36}

Rewrite

\frac{5 30 i}{36}

in standard complex form:

\frac{5 30}{36} i

= \frac{5 30}{36} i

37 \cdot 535

\frac{5 - 5}{2 + 2}

\frac{x \cdot x ^{3}}{x ^{4}}

x y^{0}

\frac{3}{8} + \frac{4}{5}

What is sqrt((-125)/(216)) ?
The solution to sqrt((-125)/(216)) is i(5sqrt(30))/(36)