What is the square root of 1?
Understand the Problem
The question is asking for the value of the square root of 1. The square root of a number is a value that, when multiplied by itself, gives the original number.
Answer
The square root of 1 is $1$ and $-1$.
Answer for screen readers
The possible values for the square root of 1 are $1$ and $-1$.
Steps to Solve
-
Definition of Square Root
The square root of a number $x$ is a value $y$ such that $y^2 = x$. In this case, we are looking for the square root of 1. -
Setting up the Equation
We want to find a number $y$ such that:
$$ y^2 = 1 $$ -
Identifying Possible Values
To solve for $y$, we take the square root of both sides:
$$ y = \pm \sqrt{1} $$
The square root of 1 could be either 1 or -1 because:
$$ 1^2 = 1 \quad \text{and} \quad (-1)^2 = 1 $$
The possible values for the square root of 1 are $1$ and $-1$.
More Information
The square root of a positive number has two solutions, one positive and one negative. For 1, both 1 and -1 satisfy the equation. This concept is crucial in understanding square roots and their properties in algebra.
Tips
One common mistake is to assume that the square root of a number is always positive. While the principal square root is typically taken as positive, it's important to remember that both positive and negative values can satisfy the square equation.
