Solving Radical Equations

The video tutorial explains how to solve a radical equation by isolating the radical, squaring both sides, and solving for x. It emphasizes the importance of verifying solutions by substituting them back into the original equation to ensure they work. The example provided results in a single solution, x = 81, which is verified to be correct.

What is the first step in solving a radical equation?

• Add a constant to both sides

• Isolate the radical

• Multiply both sides by a number

• Subtract a constant from both sides

Why is it important to isolate the radical before squaring both sides?

• To simplify the equation

• To ensure the solution is correct

• To avoid extraneous solutions

• To make the equation linear

What should you do after solving for x in a radical equation?

• Check if the solution satisfies the original equation

• Add the solution to both sides

• Subtract the solution from both sides

• Multiply the solution by 2

What operation is performed after adding 2 to both sides in the given equation?

• Subtract 3 from both sides

• Multiply both sides by 3

• Divide both sides by 3

• Add 3 to both sides

What is the result of squaring both sides of the equation after isolating the radical?

• x = 3

• x = 81

• x = 27

• x = 9

How do you verify that x = 81 is the correct solution?

• By solving another equation

• By checking if it satisfies a different equation

• By substituting it back into the original equation

• By using a calculator

What is the principal root of 81?

• 8

• 9

• 10

• 7

What is the final step in verifying the solution of the radical equation?

• Dividing the result by 3

• Subtracting 2 from the result

• Multiplying the result by 3

• Adding 2 to the result

What is the value of 9 divided by 3?

• 1

• 2

• 3

• 4

What is the final value obtained after subtracting 2 from 3?

• 0

• 1

• 2

• 3