Grade 12 Math: Square and Cube Root Equations

This worksheet focuses on solving square and cube root equations, identifying extraneous solutions, and applying these concepts to various algebraic problems for Grade 12 students.

Grade 12 Math AlgebraRadical Equations and FunctionsSquare and Cube Root Equations

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Includes

2 Short AnswerFill in the BlanksMultiple ChoiceTrue / False

Standards

CCSS.MATH.CONTENT.HSA.REI.A.2CCSS.MATH.CONTENT.HSA.APR.D.6

Topics

AlgebraRadical EquationsSquare RootsCube RootsExtraneous Solutions

7 sections · Free to use · Printable

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Square and Cube Root Equations

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

1. Solve the equation: √(3x + 4) = 5

2. Find the solution(s) for: √(x - 1) + 3 = x

3. When solving radical equations, it is crucial to check for solutions, which are values that satisfy a transformed equation but not the original one.

4. The equation √(x + 2) = x - 4 has an extraneous solution of x = .

5. Solve for y: ∛(2y - 7) = 3

6. Determine the value of z in the equation: ∛(z^2 + 1) = 2

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

x = -2

x = 3

x = -3

No extraneous solutions

8. The equation √(x - 5) = -2 has no real solutions.

True

False