LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

PROPERTIES OF SQUARE OF NATURAL NUMBERS

__Some Properties Of The Squares of Natural Numbers are as follows__ –

**a) The squares of even numbers are even, while the squares
of odd numbers are odd.**

**b) Perfect squares can never end with the digits 2, 3, 7
& 8, also they cannot have an odd number of zeros at the end. For example
342, 5013, 117, 3568, 25000 are not perfect squares.**

**c) The square of a natural number (other than 1) is –**

**1) Divisible by 3 or leaves the remainder 1 when divided by 3.**

**2) Divisible by 4 or leaves the remainder 1 when divided by 4.**

**Example - 15² = 225 = 3 X 75 = 4 X 56 + 1**

** 16²
= 256 = 3 X 85 + 1 = 4 X 64**

**d) The difference of the squares of two consecutive natural
numbers is always odd and is equal to the sum of those consecutive natural
numbers.**

**Example - 7² - 6² =
49 – 36 = 13 = 7 + 6**

** 14²
- 13² = 196 – 169 = 27 = 14 + 13**

** 10²
- 9² = 100 – 81 = 19 = 10 + 9**

** 20²
- 19² = 400 – 361 = 39 = 20 + 19 **

** 15²
- 14² = 225 – 196 = 29 = 15 + 14**