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The number 1500 is reduced by the least possible amount so that it becomes a perfect square. What is the square root of the number obtained?

Class 8Squares and Square RootsSquares and Roots
  • A39
  • B38
  • C56
  • D1444

Step-by-Step Solution

The largest perfect square not exceeding 1500 is , since already overshoots. So the least amount removed is 1500 − 1444 = 56, the number obtained is 1444, and its square root is 38. The trap 39 is the root of 1521, which you reach by ADDING 21 rather than reducing. The traps 56 and 1444 answer other questions — the amount removed and the resulting square — not the root that was asked for.
Answer: B) 38

Key idea: Properties of perfect squares

Useful patterns to spot a perfect square (and reject non-squares):

- **Last digit**: a perfect square ends in 0, 1, 4, 5, 6, or 9 — NEVER in 2, 3, 7, or 8. So 142 cannot be a perfect square (ends in 2).
- **Number of zeros at the end**: must be even. 100 is a perfect square ; 1000 is not.
- **Squares of even numbers are even; squares of odd numbers are odd.**
- **Sum of consecutive odd numbers**: 1 + 3 + 5 + … + . Try it: .

These let you reject many candidates without doing any heavy work.

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