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The square of any whole number ending in 5 always ends in 25. Using this clue, which of the numbers below IS actually the square of a whole number ending in 5?

Class 8Squares and Square RootsSquares and Roots
  • A2525
  • B5625
  • C4525
  • D6525

Step-by-Step Solution

All four end in 25, but that test only REJECTS candidates — it never confirms a square. Checking: . The other three fall strictly between consecutive squares (2500 < 2525 < 2601, 4489 < 4525 < 4624, 6400 < 6525 < 6561), so none of them is a perfect square. Ending in 25 is necessary, not sufficient.
Answer: B) 5625

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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