Table of Contents
- Squares of 2 Consecutive Numbers
- Summary
- What’s Next?
In the previous segment, learnt about the sum of Triangular numbers. In this segment, we will look at numbers between 2 consecutive square numbers.
What pattern is seen between squares of two consecutive numbers?
Before we look at the patterns, we need to understand that, consecutive square numbers are the squares of consecutive numbers.
For example, 4 and 9 are consecutive squares. And they are the squares of 2 and 3, which are consecutive numbers.
Now, let us look at a couple of patterns seen in consecutive numbers and their squares.
Pattern 1
The number of non-square numbers between two consecutive square numbers is one less than the difference between these squares.
Examples
- Consider the consecutive squares 4 and 9.
As per the rule, the number of non-square numbers between these two numbers is: (9 – 4) – 1 = 5 – 1 = 4.
Let us verify this.
The numbers between 4 and 9 are 5, 6, 7, 8. That is 4 numbers. And all these 4 numbers are non-square. Hence the rule holds true.
- Here is another example; 9 and 16
The number of non-square numbers between 9 and 16 is given by: (16 – 9) – 1 = 7 – 1 = 6
Let us verify this.
