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3000 is not a perfect square. It can be turned into one either by adding a number to it or by taking a number away from it. Which of these is the SMALLER change?

Class 8Squares and Square RootsSquares and Roots
  • ASubtract 84
  • BAdd 84
  • CSubtract 25
  • DAdd 25

Step-by-Step Solution

and , so 3000 lies between them. Climbing up needs 3025 − 3000 = 25; dropping down needs 3000 − 2916 = 84. Since 25 < 84, adding 25 is the smaller change. The other three options pair a correct number with the wrong direction — always check whether the number you found came from the square ABOVE or the square BELOW.
Answer: D) Add 25

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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