Page 3 - Lesson Notes

 There are 2n non perfect square numbers between the squares of the numbers n
and (n + 1).
2
2
Example: Non perfect square numbers between 7 and 8 is 2n= 2*7= 14.

Adding odd numbers:

 So we can also say that if a natural number cannot be expressed as a sum of
successive odd natural numbers starting with 1, then it is not a perfect square.

Sum of consecutive natural numbers:

Square of any odd number can be expressed as sum of two consecutive natural
2
2
2
number. N = −1 + +1
2 2