Algebra 2 Practice Test: Radical Equations
- Radical Equations
- 10 questions
- 15 minutes
These 10 questions practice solving equations with square roots, cube roots and rational exponents. Isolate the radical before you square, and check every answer in the original equation because squaring can create extraneous solutions.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
Solve x + 5 = 4.
Correct answer: B
Square both sides: x + 5 = 16, so x = 11. Check: 16 = 4. Forgetting to square 4 gives x = −1.
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Question 2
Solve 2x − 1 + 3 = 8.
Correct answer: A
Isolate the root first: 2x − 1 = 5. Then 2x − 1 = 25 and x = 13. Not squaring 5 gives 2x − 1 = 5 and x = 3.
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Question 3
What is the solution set of x + 7 = x + 1?
Correct answer: A
Squaring gives x + 7 = x2 + 2x + 1, so x2 + x − 6 = 0 and x = 2 or x = −3. For x = −3 the left side is 2 and the right side is −2, so −3 is extraneous.
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Question 4
Solve ∛(x − 4) = 3.
Correct answer: D
Cube both sides: x − 4 = 27, so x = 31. Squaring instead of cubing gives 13.
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Question 5
What is the solution of 3x + 1 = −2?
Correct answer: C
A principal square root is never negative, so no real x works. Squaring would give x = 1, but 4 = 2, not −2, so 1 is extraneous.
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Question 6
Solve x3/2 = 27 for x > 0.
Correct answer: A
Raise both sides to the power 2/3: x = 272/3 = (∛27)2 = 32 = 9. Check: 93/2 = 33 = 27.
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Question 7
Solve x + 2 = x.
Correct answer: B
Write x = x − 2 and square: x = x2 − 4x + 4, so x2 − 5x + 4 = 0 and x = 1 or 4. For x = 1 the left side is 3, not 1, so only 4 works.
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Question 8
Solve 5x − 4 = x + 8.
Correct answer: C
Square both sides: 5x − 4 = x + 8, so 4x = 12 and x = 3. Check: both sides equal 11.
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Question 9
An object dropped from a height of h feet hits the ground at a speed of about v = 64h feet per second. At what height was an object dropped if it hits the ground at 48 feet per second?
Correct answer: B
Square both sides: 482 = 64h, so 2,304 = 64h and h = 36. Dividing 48 by 64 without squaring gives 0.75.
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Question 10
The equation x + 10 = x − 2 has one real solution and one extraneous solution. Which number is the extraneous solution?
Correct answer: D
Squaring gives x2 − 5x − 6 = 0, so x = 6 or x = −1. For x = −1 the left side is 3 and the right side is −3, so −1 is extraneous, while 6 checks: 16 = 4.
Questions you leave blank are not counted as wrong.
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