Question

Explain why any even root of a negative number is not a real number, but an odd root of a negative number is a real number.

Answer 1

let i=sqrt(-1)
then i^2= real number
i^3= realnumber*sqrt(-1)
and so on i^2n always real
and i^3n always has sqrt(-1) as a factor

Answer 2

a negative number, multiplied an odd number of times, is still negative

no real number, multiplied an even number of times, can be still negative

pos times pos is pos
neg times neg is pos