A square root of a number $a$ is a number that, when multiplied by itself, equals $a.$ For example, $4$ and $\text{-}4$ are the square roots of $16.$ All positive numbers have two square roots — one positive and one negative. To avoid ambiguity, when talking about the square root of a number, only the positive root, also known as its principal root, is considered. Furthermore, to denote the square root, the symbol 4​ is used. For example, the square root of $16$ is denoted as $\sqrt{16}.$ In the example above, the principal root of $16$ is $4$ because $4$ multiplied by itself equals $16$ and $4$ is positive. When a number is a perfect square, its square roots are integers. The square roots of positive integers that are non-perfect squares are irrational numbers.

Principal Root of Perfect Squares		Principal Root of Non-Perfect Squares
Perfect Square	Principal Root (Integer Number)	Non-Perfect Square	Principal Root (Irrational Number)
$1$	$\sqrt{1}=1$	$2$	$\sqrt{2}\approx 1.414213\dots$
$4$	$\sqrt{4}=2$	$3$	$\sqrt{3}\approx 1.732050\dots$
$9$	$\sqrt{9}=3$	$5$	$\sqrt{5}\approx 2.236067\dots$
$16$	$\sqrt{16}=4$	$10$	$\sqrt{10}\approx 3.162277\dots$
$25$	$\sqrt{25}=5$	$20$	$\sqrt{20}\approx 4.472135\dots$

The square root of a negative number is not a real number. This is because there is no real number that, when multiplied by itself, results in a negative number. Instead, the square roots of negative numbers are imaginary numbers.