Solving Radical Equations: Square and Cube Roots

What is the first step in solving a radical equation?

• Add a constant to both sides

• Multiply both sides by 2

• Isolate the radical

• Subtract a constant from both sides

In the first example, what operation is used to eliminate the square root?

• Cubing both sides

• Squaring both sides

• Multiplying by the reciprocal

• Taking the fourth root

After isolating the square root in the first example, what is the next step?

• Divide both sides by 2

• Square both sides

• Subtract 1 from both sides

• Add 1 to both sides

In the second example, what power is used to eliminate the cube root?

• Third power

• Fifth power

• Second power

• Fourth power

What is the result of raising 3 to the third power?

• 9

• 27

• 243

• 81

What are extraneous solutions?

• Solutions that satisfy the original equation

• Solutions that do not satisfy the original equation

• Solutions that are always positive

• Solutions that are always negative

In the example involving a quadratic equation, what are the two possible solutions?

• x = 4 and x = -1

• x = -3 and x = 2

• x = -4 and x = 1

• x = 3 and x = -2

What must be true about the number under a square root for it to be valid?

• It can be any real number

• It must be negative

• It must be positive

• It must be zero

In the final example, what is the correct solution after factoring the quadratic equation?

• x = 5 and x = -3

• x = 3 and x = -5

• x = 5

• x = -3

What is the first step in solving a cube root radical equation?

• Cube both sides

• Divide by the coefficient

• Square both sides

• Move the constant to the other side