Some more patterns in square numbers

Table of Contents

• Patterns in Square Numbers
  • Example 1
  • Example 2
• What’s Next?

In the previous segment, we looked at the pattern seen in the product of two consecutive even or odd natural numbers. In this segment, we will look at a few more patterns in square numbers.

Patterns in square numbers

We have looked at quite a few patterns in square numbers. We will look at a few more interesting patterns.

Example 1

Consider the number series, 1, 11, 111, 1111, 11111, 111111 and so on. This is what the squares of the numbers look like:

1² = 1

11² = 121

111² = 12321

Let us understand the pattern with the number 1111. Count the number of 1s. In this case, it is 4.

The first digits of the square will be, 1, 2, 3, 4.

And then we write the digits in descending order, which is 3, 2, 1. So, 1111² = 1234321

Similarly, the squares in the series can be written as:

11111² = 123454321

111111² = 12345654321

This pattern helps in finding the squares of any big number having all the digits 1.