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
A number is 25. After subtracting successive odd numbers starting from 1, what happens?
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It reaches 0 after 5 steps
25 − 1 = 24, 24 − 3 = 21, 21 − 5 = 16, 16 − 7 = 9, 9 − 9 = 0. So 25 is a perfect square.
A cube number is 1728. What is its cube root?
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12
1728 = 12 × 12 × 12. So its cube root is 12.
A number has prime factorisation 2 × 2 × 3. What is the prime factorisation of its cube?
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2³ × 2³ × 3³
Each prime factor appears three times in the prime factorisation of its cube. So, 12³ = 2³ × 2³ × 3³.
A number has 38 as its value. After subtracting successive odd numbers from 1, what is the result?
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It goes below 0 without reaching exactly 0
38 − 1 = 37, 37 − 3 = 34, 34 − 5 = 29, 29 − 7 = 22, 22 − 9 = 13, 13 − 11 = 2, 2 − 13 = −11. It does not reach exactly 0.
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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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