Mock Test-3 Chapter-1| Ganita Prakash | Grade 8 :A Square and A Cube

Mock Test – Perfect Cubes & Cube Roots (Class 8 Math)

Hello! This mock test is designed to check your understanding of perfect cubes and cube roots, covered in Chapter 1 of Class 8 Maths. Work through the problems and then compare your answers with the key below!

Instructions: Try to solve all questions yourself first. After that, check the answer key and explanations at the end.

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Mock Test Questions

1. Cube roots by factorisation

   Find the cube roots of:

   1. 512
   2. 64000

2. Make it a perfect cube

   By what smallest number should 108 be multiplied so that the product becomes a perfect cube?

3. True or False? Give a short reason.

   1. The cube of any even number is even.
   2. There is no perfect cube that ends with the digit 2.
   3. The cube of a negative number is positive.
   4. A perfect cube can have exactly three zeros at the end.
   5. The cube of any 2‑digit number has at least 4 digits.

4. Guess cube roots without factorisation

   You are told that each of these numbers is a perfect cube. Guess the cube root of each, without doing full prime factorisation:

   1. 2197
   2. 2744
   3. 4096
   4. 6859

5. Which is the greatest?

   Which of the following has the greatest value? Explain briefly.

   1. 67^3 - 66^3
   2. 43^3 - 42^3
   3. 67^2 - 66^2
   4. 43^2 - 42^2

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Answer Key & Explanations

1. Cube roots

   1. 512 = 8 x 8 x 8. Cube root is 8.
   2. 64000 = 40 x 40 x 40. Cube root is 40.

2. Make it a perfect cube

   Prime factorisation of 108 is 2 x 2 x 3 x 3 x 3 (2^2 x 3^3). The factor 3 is already a triplet, but the factor 2 needs one more term to become a triplet (2^3).

   The smallest number to multiply by is 2.

3. True or False

   1. True. (Even x Even x Even is always Even.)
   2. False. (Example: 8^3 = 512, which ends in 2.)
   3. False. (The cube of a negative number is negative. Example: (-3)^3 = -27.)
   4. True. (Any cube of a number ending in 0 must have groups of three zeros. Example: 10^3 = 1000.)
   5. True. (The smallest 2-digit number is 10, and 10^3 = 1000, which has 4 digits.)

4. Guessing cube roots

   1. 2197: Ends in 7 (from 3^3). Remaining part is 2 (from 1^3). Cube root: 13.
   2. 2744: Ends in 4 (from 4^3). Remaining part is 2 (from 1^3). Cube root: 14.
   3. 4096: Ends in 6 (from 6^3). Remaining part is 4 (from 1^3). Cube root: 16.
   4. 6859: Ends in 9 (from 9^3). Remaining part is 6 (from 1^3). Cube root: 19.

5. Greatest expression

   The greatest value is (i) 67^3 - 66^3.

   Reasoning: Differences between consecutive cubes are always much larger than differences between consecutive squares. Therefore, (i) and (ii) are greater than (iii) and (iv). Since the value of the difference in cubes (a^3 - b^3) increases significantly as 'a' increases, the difference starting with 67 (i) will be the largest.