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Q1. In Queen Ratnamanjuri's puzzle the kth servant toggles every locker whose number is
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Q2. Khoisnam observes that some lockers were toggled exactly twice — these are the passcode lockers. Which numbered lockers were toggled exactly twice?
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Q3. The square idea extends to fractions and decimals. The value of (2.5)² is
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Q4. On the textbook defines a square number. Which of the following is the textbook's definition?
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Q5. The rule: if a number ends in 6, its square also ends in 6. Which of these squares ends in 6?
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Q6. Rohini reads that the square of an even number is even and the square of an odd number is odd. Without computing, she can say that 137² is
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Q7. The difference between consecutive squares is always odd. The value of 15² − 14² is
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Q8. Between n² and (n + 1)² there are exactly 2n non-square numbers. How many non-square numbers lie between 12² and 13²?
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Q9. Two consecutive triangular numbers add up to a square — for example, 1 + 3 = 4 and 3 + 6 = 9. The sum 10 + 15 equals
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Q10. Priya uses the listing-of-squares method to find √576. She lists 20² = 400, 21² = 441, 22² = 484, 23² = 529, 24² = 576. Therefore √576 is
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Q11. Aman uses repeated-subtraction method on 81: 81 − 1 = 80, 80 − 3 = 77, 77 − 5 = 72, … He stops when the result is 0. The number of subtractions he performed equals
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Q12. A square garden has area 441 sq metres. Using prime factorisation in pairs, what is the length of one side of the garden?
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Q13. Asks how many 1 cm cubes are needed to make a larger cube of edge 2 cm. The answer is
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Q14. The first few perfect cubes. The value of 5³ is
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Q15. The cube root of 1000 using the inverse-of-cubing idea. The cube root of 1000 is
