Squares and Cubes (Class 8)

What this worksheet covers

This is an eighteen-question practice worksheet on squares, square roots, cubes and cube roots for Class 8, written to the pattern of the SOF International Mathematics Olympiad (IMO). It carries 24 marks and is designed to be attempted in 45 minutes, split across three sections — Mathematical Reasoning, Everyday Mathematics and Reasoning and Achievers Section. Every question is multiple choice with exactly one correct option, and every one comes with a fully worked solution rather than just an answer key — so a child who gets one wrong can see where the reasoning went astray instead of only learning that it did.

Skills your child practises

• Applied problem-solving on squares, square roots, cubes and cube roots at Class 8 level
• Working accurately against a time limit, as the real paper demands
• Mathematical Reasoning questions in the olympiad format
• Everyday Mathematics and Reasoning questions in the olympiad format
• Achievers Section questions in the olympiad format
• Reading worked solutions to find the step that went wrong

How to use it

1. 1There are 18 questions in this worksheet. All questions are compulsory.
2. 2Each question has four options (A), (B), (C) and (D). Exactly one option is correct.
3. 3Questions 1–15 carry 1 mark each. Questions 16–18 (Achievers Section) carry 3 marks each.
4. 4There is no negative marking. Use of a calculator is not allowed.
5. 5Rough work may be done on the blank space at the side of each page.

Sample questions from this worksheet

A preview of what's inside Squares and Cubes (Class 8) — the PDF has the full set, and every question comes with a worked solution like these.

1. 1. Which of the following is a perfect square?

   • A121correct
   • B122
   • C123
   • D124
   Solution: 121 = 11 × 11 = 11², so it is a perfect square. The others lie between 11² = 121 and 12² = 144 and are therefore not perfect squares.

2. 2. What is the smallest number by which 252 must be multiplied so that the product is a perfect square?

   • A3
   • B5
   • C7correct
   • D9
   Solution: Prime factorise: 252 = 2 × 2 × 3 × 3 × 7 = 2² × 3² × 7.
   For a perfect square every prime must appear an even number of times. Here 7 appears once, so we multiply by 7, giving 1764 = 42².

3. 3. Consider the following statements.(i) The square of every odd number is odd.(ii) √a × √b = √(ab) for all positive numbers a and b.(iii) Every natural number has a natural number as its square root.Which of the statements is/are correct?

   • A(i) and (ii) onlycorrect
   • B(ii) and (iii) only
   • C(i) and (iii) only
   • DAll three
   Solution: Statement (i) is true — an odd number is 2k + 1 and its square 4k² + 4k + 1 is again odd. Statement (ii) is true for positive a and b, for example √4 × √9 = 2 × 3 = 6 = √36. Statement (iii) is false; √2 is not a natural number. Hence (i) and (ii).