Algebra 1 Practice Test: Simplifying Radicals
- Simplifying Radicals
- 10 questions
- 13 minutes
These 10 questions practice simplifying square roots and working with radical expressions. Look for the largest perfect square factor, such as 4, 9, 16, 25 or 36.
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
Simplify 72.
Correct answer: C
The largest perfect square factor of 72 is 36: 36 · 2 = 62. 63 would equal 108.
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Question 2
Simplify 50 + 18.
Correct answer: A
Simplify each root first: 52 + 32 = 82. You cannot add the numbers under the roots, so 68 is wrong.
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Question 3
Simplify 6 · 15.
Correct answer: B
Multiply under one root: 90 = 9 · 10 = 310. 21 adds 6 and 15 instead of multiplying them.
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Question 4
What is the value of (23)2?
Correct answer: D
Square both factors: 22 · (3)2 = 4 · 3 = 12. Squaring only the 2 gives 43.
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Question 5
Rationalize the denominator: 63.
Correct answer: A
Multiply top and bottom by 3: 633 = 23. Forgetting to divide 6 by 3 leaves 63.
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Question 6
Simplify 48x4 for x ≥ 0.
Correct answer: C
48 = 16 · 3 = 43 and x4 = x2. Taking a square root halves the exponent, so x4 becomes x2, not x. -
Question 7
Simplify 35 − 75.
Correct answer: D
Like radicals combine like like terms: (3 − 7)5 = −45. The radicand stays 5; it is not added to itself.
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Question 8
Multiply (5 + 2)(5 − 2).
Correct answer: B
This is a difference of squares: (5)2 − 22 = 5 − 4 = 1. The middle terms −25 and +25 cancel.
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Question 9
Which number is between 7 and 8?
Correct answer: C
Since 72 = 49 and 82 = 64, a square root lies between 7 and 8 only if the radicand is between 49 and 64. Only 56 fits.
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Question 10
Simplify 52 + 122.
Correct answer: A
Add first: 25 + 144 = 169, and 169 = 13. Taking the roots separately (5 + 12 = 17) is not allowed, since a square root does not split over addition.
Questions you leave blank are not counted as wrong.
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