# What is the square root of 25 ?

Feb 24, 2017

$5$

#### 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.