What is the square root of $25$ ?

Question

3733 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-24T22:48:42

$5$

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.

What is the square root of 2525 ?