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 as:

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

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.

When $\sqrt x$ is written, then by convention this refers to the positive square root of $x$.

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