Chapter 1
Linear Equations and Graphing
Course: Gre
Subject: Gre Quantitative Reasoning
Chapter: Foundations Of Functions And Composition
Introduction: Solving Equations with Squares
Many equations involve squared variables—x² = 9, (x - 3)² = 25, or ax² = c. The square root property provides a direct method for solving such equations without expanding or factoring.
What Is the Square Root Property?
The Square Root Property states:
If x² = c, then x = √c or x = -√c
Where c is a non-negative number.
In other words, if a variable is squared and equal to a constant, the variable equals either the positive or negative square root of that constant.
The Square Root Formula
The Square Root Formula is derived directly from the property:
x² = c → x = ±√c
The ± symbol (read as "plus or minus") indicates that both the positive and negative square roots are solutions.