Properties of Cubes Quiz - CBSE Class 8 Mathematics
Free practice quiz: Properties of Cubes (CBSE Class 8 Mathematics). 13 multiple-choice questions with answers and explanations. Play online, no sign-up needed.
This CBSE Class 8 Mathematics practice quiz has 13 multiple-choice questions on Properties of Cubes, and 13 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.
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Perfect cubes and prime factor groups
- A number is a perfect cube if its prime factors form complete groups of three equal primes.
- For the smallest perfect cube multiple, multiply by exactly the primes needed to complete every incomplete group.
- Or divide by the leftover primes to get a smaller number that is a perfect cube.
Common mistake: Multiplying by the whole leftover group instead of only the missing primes, so the result is a cube but not the smallest.
Odd, even and unit digits
- The cube of an odd number is odd; the cube of an even number is even.
- The unit digit of a cube depends only on the unit digit of the original number.
- Numbers ending in 0, 1, 4, 5, 6 or 9 have cubes ending in that same digit.
Common mistake: Assuming every cube ends in the same digit as its number. The other four digits swap in pairs; cube a small number to see.
Sum and difference of cubes
- A difference of two cubes always factorises with (a − b) as one factor.
- A sum of two cubes always factorises with (a + b) as one factor.
- So a³ + b³ is always divisible by a + b.
Common mistake: Mixing up signs. The ab term in the second bracket has the opposite sign to the first bracket: (a − b) pairs with +ab.
Cube roots and cube volume
- The cube root of n is the number that, used as a factor three times, gives n.
- A cube with side s has volume s³, so side length equals the cube root of the volume.
- Some numbers are both squares and cubes, like 64, which equals 4³ and 8².
Common mistake: Dividing by 3 to find a cube root. The cube root of a number is not one-third of it.
Exam tips
- Verify a cube root by raising your answer to the third power.
- Use the unit digit of a cube to quickly narrow down the unit digit of its cube root.
- For the smallest cube divisible by a number, raise each prime's power to the next multiple of 3.
Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.
Sample questions
Which of the following numbers is a perfect cube?
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Answer: A. 8
8 is a perfect cube because 2 x 2 x 2 = 8.
What is the smallest perfect cube that is divisible by 9?
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Answer: A. 27
27 is a perfect cube (3³) and is divisible by 9 (27/9 = 3).
What is the sum of the cubes of the first three natural numbers?
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Answer: D. 36
1³ + 2³ + 3³ = 1 + 8 + 27 = 36
If n is a natural number, then n³ + 1 is divisible by which of the following?
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Answer: A. n+1
Use the identity a³ + b³ = (a+b)(a²-ab+b²). Here, a=n and b=1. Thus, n³+1 = (n+1)(n²-n+1)
Find the smallest number by which 1728 must be multiplied to make it a perfect cube.
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Answer: A. 1
1728 = 12³ Therefore, it is already a perfect cube.
More questions in this quiz
Answers and explanations are in the full quiz.
- The cube of an odd number is always:
- Find the value of ∛(216 x 125)
- If the unit digit of a number is 2, what will be the unit digit of its cube?
- Find the number whose cube is 1331.
- What is the value of (100³ - 99³)?
- If x³ - y³ = 189 and x - y = 3, find the value of x² + xy + y²
- A number is multiplied by itself twice. The result is 2744. Find the number and prove it's a perfect cube.
- The volume of a cube is 1728 cubic centimeters. What is the length of its side, and is this length a perfect square?
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