Solving Square Root Equations

Front

What is a square root equation?

Back

An equation that involves a variable under a square root, typically in the form of √x = a.

Front

How do you isolate the square root in an equation?

Back

To isolate the square root, move all other terms to the opposite side of the equation.

Front

What is the first step in solving a square root equation?

Back

Square both sides of the equation to eliminate the square root.

Front

What does it mean if a square root equation has two solutions?

Back

It means that there are two values of the variable that satisfy the equation.

Front

What is an extraneous solution?

Back

An extraneous solution is a solution that does not satisfy the original equation after checking.

Front

How can you check if a solution is valid for a square root equation?

Back

Substitute the solution back into the original equation to see if it holds true.

Front

What is the significance of negative solutions in square root equations?

Back

Negative solutions may arise from squaring both sides, but they must be checked against the original equation.

Front

What is the range of solutions for the equation √x = 5?

Back

The solution is x = 25, and x must be non-negative.

Front

What happens if you square both sides of an equation incorrectly?

Back

You may introduce extraneous solutions that do not satisfy the original equation.

Front

How do you graph the solutions of a square root equation?

Back

Plot the points on a coordinate plane and identify the x-values that satisfy the equation.