Why take this quiz? It's a great way to revise key concepts like last digit patterns, LCM for perfect squares, and comparing powers. Plus, we've included an answer key at the end for self-assessment. Downloadable PDF version coming soon! If you're searching for grade 8 math quiz questions or squares and cubes practice test, you've come to the right place.
Mock Test Quiz: Squares and Cubes (Class 8 | Chapter - 1)
Total Marks: 13 | Time: 30 minutes
Part A: Perfect Squares (5 marks)
1. Identify Non-Perfect Squares (1 mark)
Which of the following numbers are NOT perfect squares?
- (i) 1568
- (ii) 2025
- (iii) 3087
- (iv) 4096
2. Last Digit Pattern (1 mark)
Which one among 522, 782, 1452, 2032 has a last digit of 5?
3. Using Square Patterns (1 mark)
Given that 45² = 2025, what is the value of 46²?
- (i) 2025 + 45
- (ii) 2025 + 91
- (iii) 2025 + 46
- (iv) 2025 + 90
- (v) 2025 + 136
4. Finding Side Length (1 mark)
Find the side length of a square whose area is 625 cm².
5. LCM and Perfect Squares (1 mark)
Find the smallest perfect square number that is divisible by 6, 8, and 15.
Part B: Perfect Cubes (5 marks)
6. Identify Perfect Cubes (1 mark)
Which of the following numbers are perfect cubes?
- (i) 512
- (ii) 729
- (iii) 1000
- (iv) 1331
7. Prime Factorisation and Cubes (1 mark)
Is 2160 a perfect cube? Use prime factorisation to justify your answer.
Prime factorisation of 2160: 2⁴ × 3³ × 5
8. Finding Cube Root (1 mark)
Find the cube root of 13824 using prime factorisation.
(Hint: 13824 = 2⁹ × 3³)
9. Cube Root Estimation (1 mark)
Without calculating, guess the cube root of 2744. Explain your reasoning using the last digit pattern.
10. Taxicab-Style Problem (1 mark)
Which number can be expressed as the sum of two cubes in two different ways?
- (i) 728
- (ii) 1024
- (iii) 4104
- (iv) 5832
Part C: Mixed Concepts (3 marks)
11. Comparing Powers (1 mark)
Which is greater and by how much? 12² or 2³ + 4³?
12. Real-Life Application (1 mark)
A square garden has an area of 361 m². A rectangular path of width 2 m runs around its perimeter. What is the perimeter of the garden?
13. Prime Factorisation Application (1 mark)
What is the smallest number by which 1944 must be multiplied to make it a perfect cube? What is the cube root of the resulting number?
(Hint: 1944 = 2³ × 3⁵)
Answer Key
Q1: (i), (iii) | 1 mark
Q2: 1452 | 1 mark
Q3: (ii) 2025 + 91 | 1 mark
Q4: 25 cm | 1 mark
Q5: 3600 | 1 mark
Q6: (i), (ii), (iii), (iv) | 1 mark
Q7: No (factors not in triplets) | 1 mark
Q8: 24 | 1 mark
Q9: 14 (last digit 4 → cube root last digit 4) | 1 mark
Q10: (iii) 4104 = 2³ + 16³ = 9³ + 15³ | 1 mark
Q11: 2³ + 4³ = 72 is greater by 36 | 1 mark
Q12: 76 m | 1 mark
Q13: Multiply by 3; cube root = 18 | 1 mark
Total: 13 marks
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