Square numbers always end in 0, 1, 4, 5, 6 or 9. No square ends in 2, 3, 7 or 8. Also, squares are formed by adding consecutive odd numbers starting from 1. Only squares have odd number of factors.
Class 8 Mathematics Ganita Prakash Chapter 1 A Square and A Cube NCERT solutions
Class 8 Mathematics Chapter 1 A Square and A Cube question answer
We observe that square numbers always end with digits 0, 1, 4, 5, 6 or 9—never 2, 3, 7 or 8. Square numbers are formed by summing consecutive odd numbers starting from 1. Another pattern is that only square numbers have an odd number of factors. These patterns help in identifying whether a number is a perfect square and predicting how many toggles lockers undergo in the puzzle logic.
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