Solving Square Root Equations
This worksheet focuses on solving square root equations, including identifying extraneous solutions, for Grade 11 algebra students.
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Solving Square Root Equations
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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?
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