Square and Cube Root Equations

Square and Cube Root Equations Worksheet

Read each question carefully and solve for the variable. Remember to check for extraneous solutions where applicable.

Solve each square root equation. Show all your work.

1. √(x + 5) = 4

2. √(2x - 1) + 3 = 8

3. √(x - 3) = x - 5

Solve each cube root equation. Show all your work.

1. ³√(x - 7) = 2

2. ³√(3x + 1) - 4 = 0

3. ³√(x² + 2x) = ³√(x + 2)

1. Which of the following is an extraneous solution to the equation √(x + 6) = x?

1. When solving radical equations, it is important to always   your solutions to check for extraneous solutions.

2. An extraneous solution is a solution that arises from the process of solving an equation but is not a   of the original equation.

3. The domain of a square root function requires that the expression under the radical sign must be   than or equal to zero.

1. All solutions obtained when solving a radical equation are always valid.

2. Cube root equations do not typically produce extraneous solutions.