Solving Square Root Equations

This worksheet focuses on solving square root equations, including identifying extraneous solutions, for Grade 11 algebra students.

Grade 11 Math AlgebraSolving Square Root Equations

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Includes

2 Short AnswerTrue / FalseFill in the Blanks

Standards

CCSS.MATH.CONTENT.HSA.REI.A.2

Topics

AlgebraSquare Root EquationsExtraneous SolutionsGrade 11

6 sections · Free to use · Printable

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Solve each square root equation. Be sure to check your solutions for extraneous roots.

1. Solve for x: √(x + 5) = 3

2. Find the solution(s) to: √(2x - 1) + 4 = 7

3. Determine the value of y in: 5 - √(y + 2) = 2

Indicate whether the statement is True or False.

4. The equation √(x) = -2 has a real solution.

True

False

5. When solving √(x + 1) = x - 1, squaring both sides always leads to the correct solution(s) without introducing extraneous ones.

True

False

Fill in the blank with the correct term.

6. An solution is a solution that arises from the process of solving an equation but is not a valid solution to the original equation.

7. To check for extraneous solutions in square root equations, you must substitute your answer(s) back into the equation.

8. Solve the equation √(x - 3) = x - 5. Clearly show all steps and identify any extraneous solutions.

9. Consider the equation √(3x + 4) = x. What are the potential solutions? Which of them, if any, are extraneous?