is the square root of 27 a rational or irrational number?

Answer 1

27 = 3³ = 3² * 3

sqrt(27) = sqrt(3² * 3) = 3*sqrt(3)

sqrt(3) can't be expressed as the ratio of integers and when written as a decimal it does not terminate, so it is irrational. Thus sqrt(27) is itself irrational.