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Class 8 Perfect Cubes — practice questions with answers

Cubes and Roots · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. Which of these is a perfect cube?
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Answer: C) 64
64 = 4 x 4 x 4 = 4³, so 64 is a perfect cube. 36, 49 and 100 are perfect squares but not cubes.
2. Which of these numbers is a perfect cube?
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Answer: A) 1000
1000 = 10 x 10 x 10 = 10³, a perfect cube. The others are not cubes of whole numbers.
3. Find the smallest number by which 135 must be divided so that the quotient is a perfect cube.
(135 = 3 x 3 x 3 x 5.)
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Answer: B) 5
135 = 3³ x 5. The extra factor 5 prevents a cube, so divide by 5: 135 / 5 = 27 = 3³.
4. Meera writes the cubes 1, 8, 27, 64, 125, ... She notices the gaps between consecutive cubes: 7, 19, 37, 61, ...
What is the next gap (between 5³ and 6³)?
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Answer: D) 91
6³ - 5³ = 216 - 125 = 91.
5. Ravi claims that if you write three-digit perfect cubes, very few exist. List how many three-digit numbers (from 100 to 999) are perfect cubes.
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Answer: A) 5
Three-digit cubes are 5³=125, 6³=216, 7³=343, 8³=512, 9³=729. That is 5 numbers (4³=64 is two-digit, 10³=1000 is four-digit).
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