How do you simplify $sqrt(-75)^3$ ?

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Answer 1 · 2018-04-16T13:24:27

$color(blue)(i375sqrt(3))$

$sqrt((-75)^3)=sqrt(-1)*sqrt(75^3)$

$:.$

$sqrt(75^3)=(75)^(3/2)=(sqrt(75))^3=(sqrt(3xx25))^3=(5sqrt(3))^3$

$=5^3(sqrt(3))^3=3*5^3sqrt(3)=375sqrt(3)$

$:.$

$375sqrt(3)*sqrt(-1)=i375sqrt(3)$

$color(blue)(i375sqrt(3))$

How do you simplify sqrt(-75)^3sqrt(-75)^3?