Square Both Sides

Definition

Squaring both sides of an equation is a common algebraic technique used to solve equations involving square roots. This method involves raising both sides of the equation to the power of 2, effectively eliminating the square root and transforming the equation into a simpler form that can be more easily solved.

5 Must Know Facts For Your Next Test

1. Squaring both sides of an equation is a useful technique for solving equations that contain square roots, as it eliminates the square root and simplifies the equation.
2. This method is particularly effective when the equation contains a single variable with a square root, as squaring both sides will remove the square root and leave the variable on one side.
3. Squaring both sides preserves the equality of the equation, meaning that the solutions to the original equation and the squared equation will be the same.
4. After squaring both sides, the resulting equation may still need to be solved using additional algebraic techniques, such as combining like terms or factoring.
5. Squaring both sides is a crucial step in solving a variety of equations, including those involving perfect squares, quadratic equations, and other types of equations with square roots.

Review Questions

• Explain the purpose of squaring both sides of an equation.
  • The purpose of squaring both sides of an equation is to eliminate the square root and transform the equation into a simpler form that can be more easily solved. By raising both sides to the power of 2, the square root is removed, and the equation is reduced to a polynomial equation that can be manipulated using standard algebraic techniques, such as combining like terms or factoring.
• Describe the steps involved in solving an equation by squaring both sides.
  • To solve an equation by squaring both sides, the steps are as follows: 1) Identify the variable with a square root on one side of the equation. 2) Raise both sides of the equation to the power of 2, effectively eliminating the square root. 3) Simplify the resulting equation by combining like terms or performing other algebraic operations. 4) Solve the simplified equation for the variable of interest.
• Explain how squaring both sides of an equation preserves the equality of the original equation.
  • Squaring both sides of an equation preserves the equality because the process of raising both sides to the power of 2 does not change the underlying relationship between the expressions on each side of the equation. If the original equation was true, then the resulting equation after squaring both sides will also be true, as the square of each side maintains the same relative magnitude and relationship. This ensures that the solutions to the original equation and the squared equation will be the same.

Related terms

Equation: A mathematical statement that expresses the equality of two expressions, often used to represent a problem or relationship that needs to be solved.

Square Root: The positive value that, when multiplied by itself, gives the original number. The square root of a number is denoted by the radical symbol, $\sqrt{}$.

Isolate: The process of manipulating an equation to move a variable to one side, separating it from the other terms, in order to solve for that variable.