Question

What is the principal or(postive)square root of a number N

Answer 1

The square root of number n is a number, r, that when squared equals n.
Each positive number has two square roots, a positive one and a negative one. The principal square root of a positive number is the positive square root.

For example, this of n = 4.
There are two numbers, r, that when squared equal 4.
The are 2 and -2, since 2^2 = 4 and (-2)^2 = 4.
4 has two square roots, a positive one and a negative one.
The positive square root, 2, is the principal square root of 4.

The symbol for the principal square root is the square root symbol.

$\sqrt{4}$

means the principal square root of 4, which is 2.

If you mean the negative square root of 4, which is -2, then you must write a negative sign before the square root symbol.

$-\sqrt{4}$

means the negative square root of 4 which is -2.