Question

What is the square root of `25` ?

Answer 1

`5`

Explanation:

A square root of a number `n` is a number `x` such that:

`x^2 = n`

• Every positive number `n` has two distinct square roots, designated `sqrt(n)` (its positive, principal square root) and `-sqrt(n)`.

• Zero has one (repeated) square root, namely `0`.

• Every negative number `n` has two distinct pure imaginary square roots, namely `sqrt(-n)i` and `-sqrt(-n)i`, where `i` is the imaginary unit.

[I really dislike the term "imaginary" - such numbers are just as "real" as real numbers].

In our example we find:

`5^2 = 25`

So `sqrt(25) = 5` is the principal square root of `25` and `-5` is the other square root.