Understanding Square Root Equations

The video tutorial explains how to solve square root equations using four steps: isolating the radical, squaring both sides, solving for the variable, and checking for extraneous solutions. The example problem demonstrates these steps, revealing that the solution is extraneous. The tutorial concludes with a demonstration of using Desmos to verify solutions graphically.

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

• Solve for the variable

• Isolate the radical

• Square both sides

• Check for extraneous solutions

Why do we square both sides of the equation?

• To check for extraneous solutions

• To simplify the equation

• To isolate the variable

• To eliminate the square root

What is the result of squaring a negative number?

• An imaginary number

• Zero

• A positive number

• A negative number

What is the purpose of isolating the radical in an equation?

• To check for extraneous solutions

• To make the equation more complex

• To prepare for squaring both sides

• To simplify the equation

What is an extraneous solution?

• A solution that is always correct

• A solution that does not satisfy the original equation

• A solution that is always incorrect

• A solution that satisfies the original equation

How can you verify if a solution is extraneous?

• By checking if it is a positive number

• By checking if it is a negative number

• By checking if it satisfies the original equation

• By checking if it satisfies the squared equation

What does it mean if a solution is extraneous?

• It is not a real solution

• It is a partial solution

• It is a complex solution

• It is a valid solution

What tool can be used to graphically verify the existence of real solutions?

• Text editor

• Calculator

• Desmos

• Spreadsheet

Why might an equation have no real solution?

• Because the graph never crosses the x-axis

• Because the graph is a parabola

• Because the graph is a straight line

• Because the graph is a circle

What happens when you move all terms to one side of the equation in Desmos?

• Desmos cannot recognize the equation

• Desmos ignores the equation

• Desmos solves the equation automatically

• Desmos can graph the equation