Definition:Square Root/Positive

Definition

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

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

$\sqrt x := y \in \R_{>0}: y^2 = x$

Notation

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

• Definition:Negative Square Root

Sources

• 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 1$: Real Numbers: $\S 1.10$: Quadratic equations
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): square root