# List of equally distanced numbers in an interval [a,b] that contains both a and b

I’m writing a program that should split a given interval $$[a,b]$$ into a list of $$\sqrt{N}$$ equidistant numbers:

N = 27; a = -1; b = 1; p = 3; Range[a, b, RealAbs[b - a]/(N^(1/p) - 1)]  {-1, 0, 1} 

The result should be a list that has $$N^\frac{1}{p}$$ numbers, and that contains both $$a$$ and $$b$$. The program works when $$N=x^p$$, where $$x$$ is an integer, but fails to include $$b$$ in the list when this condition is not met.

For example, when $$p=2$$ and $$N$$ is not a perfect square:

Np = 10; a = -1; b = 1; p = 2;  Range[a, b, RealAbs[b - a]/(Np^(1/p) - 1)] // N  {-1., -0.0750494, 0.849901} 

Is there a way to specify that both ends, $$a$$ and $$b$$, should be part of the list, and then equally split the interval into a total of $$\sqrt{N}$$ equidistant numbers?