Solving Radical Equations

The video tutorial covers solving radical equations using both algebraic methods and graphing with Desmos. It begins with a simple equation, demonstrating step-by-step algebraic solutions and verification through graphing. The tutorial progresses to more complex equations, highlighting the importance of checking for extraneous solutions. The use of Desmos as a tool for verifying solutions is emphasized throughout, providing a practical approach to understanding and solving radical equations.

What is the first step in solving a radical equation algebraically?

• Isolate the variable

• Isolate the radical

• Add a constant to both sides

• Multiply both sides by a constant

How can you verify the solution of a radical equation using graphing?

• By plotting both sides of the equation and finding their intersection

• By plotting only the left side of the equation

• By checking if the graph intersects the x-axis

• By checking if the graph intersects the y-axis

What is the solution to the equation: negative 10 plus the square root of x equals negative six?

• x = 6

• x = 4

• x = 16

• x = 10

In the equation square root of x equals square root of 4 minus x, what is the value of x?

• x = 0

• x = 4

• x = 2

• x = 1

What is the purpose of squaring both sides of a radical equation?

• To simplify the equation

• To eliminate the variable

• To eliminate the radical

• To isolate the constant

What are the solutions to the equation: square root of 79 minus 5x equals x minus 11?

• x = 5 and x = 14

• x = 3 and x = 11

• x = 5 and x = 11

• x = 3 and x = 14

Why is it important to check for extraneous solutions in radical equations?

• Because they are easier to solve

• Because they simplify the equation

• Because they might not satisfy the original equation

• Because they are always correct

What is an extraneous solution?

• A solution that satisfies the equation

• A solution that does not satisfy the original equation

• A solution that is always correct

• A solution that is always incorrect

How can graphing help in identifying extraneous solutions?

• By showing all possible solutions

• By showing only the correct solutions

• By showing intersections that do not satisfy the equation

• By showing the graph of the equation

What should you do after solving a radical equation to ensure the solution is valid?

• Multiply the solution by a constant

• Graph the solution

• Add a constant to the solution

• Check the solution by substituting back into the original equation