Square and Cube Root Equations Worksheet
Grade 9 Math worksheet focusing on solving square and cube root equations, including identifying extraneous solutions.
Includes
Standards
Topics
Square and Cube Root Equations
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Read each question carefully and solve for the variable. Remember to check for extraneous solutions.
Solve each square root equation. Show all your work.
1. √(x + 5) = 3
2. √(2x - 1) = x - 2
Fill in the blank to complete the solution for the cube root equation.
3. ∛(x - 4) = 2
Cube both sides: (∛(x - 4))³ = 2³
x - 4 =
x =
4. Which of the following equations has an extraneous solution when solved?
√(x + 1) = 4
√(x - 3) = -2
∛(x) = 5
√(x + 7) = 0
Solve the following equations. Be sure to check your solutions.
5. √(3x + 4) - 2 = x
6. ∛(2x + 1) + 3 = 0
Determine if the following statements are true or false.
7. The equation √(x) = -5 has no real solutions.
True
False
8. When solving a square root equation, squaring both sides can introduce extraneous solutions.
True
False