Square and Cube Root Equations
Solve square and cube root equations, identifying extraneous solutions and understanding the domain of radical functions.
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Square and Cube Root Equations Worksheet
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Date:
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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?
x = -2
x = 3
x = -3
No extraneous solutions
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.
True
False
2. Cube root equations do not typically produce extraneous solutions.
True
False
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