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Rekha writes 1027, 3844, 5768 and 6253 on the board. Using ONLY the last-digit rule, how many of these can she immediately rule out as perfect squares?

Class 8Squares and Square RootsSquares and Roots
  • A3
  • B1
  • C2
  • D4

Step-by-Step Solution

Perfect squares end only in 0, 1, 4, 5, 6 or 9. So 1027 (ends in 7), 5768 (ends in 8) and 6253 (ends in 3) are all ruled out — that is 3 numbers. Only 3844 survives the test, and it really is a square . Answering 4 forgets that the rule cannot reject a number ending in 4.
Answer: A) 3

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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