Guided Practice
Overview
This lesson provides structured practice working with square roots, cube roots, and classifying numbers within the real number system. Apply the concepts from previous lessons.
Practice Problems
Question 1: Simplify sqrt(144).
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Answer: 12
144 = 12 x 12, so sqrt(144) = 12.
Question 2: Is sqrt(50) rational or irrational? Explain.
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Answer: Irrational
50 is not a perfect square. sqrt(50) = sqrt(25 x 2) = 5sqrt(2), which is irrational because sqrt(2) is irrational.
Question 3: Estimate sqrt(75) to the nearest whole number.
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Answer: 9 (approximately 8.66)
64 < 75 < 81, so 8 < sqrt(75) < 9. Since 75 is closer to 81, sqrt(75) is about 8.7, rounding to 9.
Question 4: Classify -7/3: natural, whole, integer, rational, or irrational?
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Answer: Rational
-7/3 is a ratio of integers, so it's rational. It's not an integer (not a whole number), not whole, and not natural.
Question 5: Simplify sqrt(72).
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Answer: 6sqrt(2)
72 = 36 x 2 = 6^2 x 2. So sqrt(72) = sqrt(36) x sqrt(2) = 6sqrt(2).
Question 6: Between which two consecutive integers does sqrt(40) lie?
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Answer: Between 6 and 7
36 < 40 < 49, so 6 < sqrt(40) < 7.
Question 7: Is pi + 2 rational or irrational?
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Answer: Irrational
The sum of an irrational number (pi) and a rational number (2) is always irrational.
Question 8: What is the cube root of 125?
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Answer: 5
5 x 5 x 5 = 125, so the cube root of 125 is 5.
Question 9: Order from least to greatest: sqrt(10), 3.5, pi
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Answer: pi, sqrt(10), 3.5
pi is about 3.14, sqrt(10) is about 3.16, and 3.5 = 3.5. So: 3.14 < 3.16 < 3.5.
Question 10: Simplify sqrt(18) + sqrt(8).
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Answer: 5sqrt(2)
sqrt(18) = 3sqrt(2) and sqrt(8) = 2sqrt(2). So 3sqrt(2) + 2sqrt(2) = 5sqrt(2).