# Definition:Square Root/Positive

< Definition:Square Root(Redirected from Definition:Square Root of Real Number)

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## Contents

## 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

## Sources

- 1977: K.G. Binmore:
*Mathematical Analysis: A Straightforward Approach*... (previous) ... (next): $\S 1$: Real Numbers: $\S 1.10$: Quadratic equations