Solving Radical Equations Worksheet
A Grade 11 worksheet focused on solving radical equations, including those with extraneous solutions, aligned with Common Core Algebra standards.
Includes
Standards
Topics
Solving Radical Equations
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Read each question carefully and solve for the variable. Remember to check for extraneous solutions.
Solve each equation. Show all your work.
1. √(x + 5) = 4
2. √(2x - 1) = 7
Solve each equation. Be sure to check for extraneous solutions.
3. x = √(x + 12)
4. x - 2 = √(x + 10)
5. Which of the following is an extraneous solution for the equation √(3x + 4) = x?
x = 4
x = -1
Both x = 4 and x = -1
Neither x = 4 nor x = -1
Complete the steps to solve the equation. Fill in the blanks.
6. Solve: √(4x - 3) = x - 2
Step 1: Square both sides: (√(4x - 3))² = (x - 2)²
Step 2: Simplify: 4x - 3 =
Step 3: Rearrange into a quadratic equation: = 0
Step 4: Factor or use the quadratic formula: x = or x =
Step 5: Check for extraneous solutions. The valid solution(s) is/are:
Solve the equation. Show all your work and check for extraneous solutions.
7. √(x + 7) - 1 = x