A Square and A Cube
CBSE · Class 8 · Mathematics
Most important questions from A Square and A Cube for CBSE Class 8 Mathematics board exam 2026. MCQs, short answer, and long answer questions with marks.
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Sample Questions
Which of the following are perfect squares?
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36, 49, 64
36 = 6², 49 = 7², and 64 = 8² are perfect squares. 50 and 72 cannot be expressed as n² for any natural number n.
Which digits can appear in the units place of a perfect square?
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0, 1, 4, 5, 9
Perfect squares can only end in 0, 1, 4, 5, 6, or 9. They never end in 2, 3, 7, or 8. For example: 1² = 1, 2² = 4, 3² = 9, 4² = 16, 5² = 25.
If 15² = 225, what is 16²?
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256
Using the pattern: 16² = 15² + (2 × 15 × 1) + 1² = 225 + 30 + 1 = 256. Alternatively, 16² = 16 × 16 = 256.
How many perfect squares are there between 1 and 100 (inclusive)?
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10
Perfect squares from 1 to 100 are: 1², 2², 3², 4², 5², 6², 7², 8², 9², 10² = 1, 4, 9, 16, 25, 36, 49, 64, 81, 100. That's exactly 10 perfect squares.
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Sources & Official References
- NCERT Official — ncert.nic.in
- CBSE Academic — cbseacademic.nic.in
- CBSE Official — cbse.gov.in
- National Education Policy 2020 — education.gov.in
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