Definition:Square Root/Positive

From ProofWiki
Jump to navigation Jump to search


Let $x \in \R_{> 0}$ be a (strictly) positive real number.

The positive square root of $x$ is the number defined and denoted as:

$\sqrt x := y \in \R_{>0}: y^2 = x$


Note that, by convention, the symbol $\sqrt x$ always refers specifically to the positive square root of $x$.

Hence, while you may encounter the notation $+\sqrt x$ for the same concept, the $+$ sign is strictly speaking unnecessary.

Also known as

The positive square root is sometimes also referred to as the principal square root, but it is usually preferred that this terminology be reserved for square roots of a complex number.

Also see