How to Identify Perfect Square
There are three rules that we need to check to find if a number is a perfect square:
Rule 1:
- There should be 1, 4, 5, 6, 9 or 0 at one’s (last) digit space of the number to be checked.
Example:
(i) 49 = (7)2
(ii) 121 = (11)2
Rule 2:
- (i) If 1, 4 or 9 is at one’s (last) digit space. Then the digit at ten’s (second last) place should be an even number or 0.
Example:
(i) 81 = (9)2
(ii) 169 = (13)2
- (ii) If 6 is at one’s (last) digit space. Then digit at ten’s (second last) place should be an odd number.
Example:
(i) 196 = (14)2
(ii) 36 = (6)2
(iii) If 5 is at one’s(last) digit place. Then digit at ten’s (second last) place should be 2.
Example:
(i) 25 = (5)2
(ii) 625 = (25)2
Rule 3:
- The digit sum of a perfect square should be an odd number or 4.
Example:
(i) 49
= 4 + 9 = 13 = 1 + 3 = 4
So, digital sum of 49 is 4. So it is a perfect square.
(ii) 196
= 1 + 9 + 6 = 16 = 1 + 6 = 7
So, the digital sum of 196 is an odd number. So, it is a perfect square.
Note: If all three conditions are satisfied then only a number is said to be a perfect square.
Perfect Square Formula
Perfect Square Formula: A polynomial or number which when multiplied by itself is called a perfect square. The perfect square is calculated by two algebraic expressions that include: (a + b)² = a² + 2ab + b² and (a – b)² = a² – 2ab + b².
In this article, we have covered the perfect square definition, how to identify perfect square, perfect square formulas, and other related topics in detail.
Table of Content
- What is the Perfect Square Formula?
- How to Identify Perfect Square
- Perfect Square Formula
- Proof of Perfect Square Formula
- Perfect Squares from 1 to 100
- Perfect Square Examples