- A16
- B15
- C125
- D25
Step-by-Step Solution
, so is between 15 and 16. 250 is much closer to 256 (6 away) than to 225 (25 away), so (actually 15.8).
Answer: A) 16
On the number line, 250 lies between two perfect squares. What is √250, correct to the nearest whole number?
Class 8Squares and Square RootsSquares and Roots
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.
- **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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