Perfect squares are the squares of natural numbers: \(1, 4, 9, 16, 25, 36, ...\)
Patterns in Perfect Squares
Unit Digit of a Square Number:
A square number can end only in \(0, 1, 4, 5, 6\) or \(9\). It cannot end in \(2, 3, 7\) or \(8\).
Let's learn and remember the property in detail.
| Unit digit of a number | Unit digit of the square number |
| \(1\) or \(9\) | \(1\) |
| \(2\) or \(8\) | \(4\) |
| \(3\) or \(7\) | \(9\) |
| \(4\) or \(6\) | \(6\) |
| \(5\) | \(5\) |
| \(0\) | \(0\) |
Important!
- \(46\) cannot be a square because it ends in \(6\), but is not formed by a perfect square number. The units digit can only help us identify numbers that are not perfect squares.
- End with zeros: Perfect squares can only have an even number of zeros at the end. For example: \(20^2 = 400\) - two zeros & \(800 = 640000\) - four zeros.
- An even number ends with an even square number. An odd number ends with an odd square number. For example: \(12^2 = 144\) - even & \(21^2 = 441\) - odd.
Reference:
National Council of Educational Research and Training (2025). Maths - Standard 8. Ganita Prakash, Part I. A square and a cube - 1.1 Square Numbers (pg. 3-5). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.