Can the root of 1 be written as 1?

Understanding the Square Root of 1

When diving into fundamental mathematics, a common point of confusion revolves around the square root of 1. While it is true that multiplying −1 by itself yields 1, the standard mathematical convention for the radical symbol (√) is strictly defined. By definition, the square root symbol always denotes the principal, non-negative value of a number.

Because of this rule, √1 equals 1, not −1. The same logic applies when expressing square roots as fractional exponents: the expression 1^1/2 consistently evaluates to 1. While an equation such as x² = 1 has two distinct real solutions (1 and −1), the square root function itself remains strictly positive, making 1 its sole output.