Solve each equation using the square root property. See Example 2. x² = 121

Verified step by step guidance

1. Identify that the equation is in the form \(x^2 = c\), where \(c\) is a positive number, which allows the use of the square root property.
2. Apply the square root property, which states that if \(x^2 = c\), then \(x = \pm \sqrt{c}\).
3. Take the square root of both sides of the equation: \(x = \pm \sqrt{121}\).
4. Simplify the square root expression by finding the number whose square is 121.
5. Write the two possible solutions for \(x\) based on the positive and negative roots.

Key Concepts

Square Root Property

The square root property states that if x² = k, then x = ±√k. This means to solve an equation where a variable is squared, you take the square root of both sides, considering both positive and negative roots.

Isolating the Variable Term

Before applying the square root property, the equation must be arranged so that the squared term is alone on one side. This ensures you can directly take the square root of both sides without additional terms complicating the process.

Simplifying Square Roots

After taking the square root, simplify the radical if possible. For perfect squares like 121, the square root is an integer (11), making the solution straightforward. Understanding how to simplify roots helps in finding exact solutions.