Square of three digit number whose digits are same

Square of three digit number whose digits are same

Let us consider the 3-digit number as aaa. Let’s see how the square of the number looks like:

https://www.hamaraguru.com/assets/files/2018-01-09/1515482634-516483-imgur-11.jpeg
Examples:

\( 111^{2} \) = \( 1^{2} \) / 2\( (1^{2}) \) / 3\( (1^{2}) \) / 2\( (1^{2}) \) / \( 1^{2} \) = 1 / 2 / 3 / 2 / 1 = 12321

 

\( 222^{2} \) = \( 2^{2} \) / 2\( (2^{2}) \) / 3\( (2^{2}) \) / 2\( (2^{2}) \) / \( 2^{2} \) = 4 / 8 / 12 / 8 / 4 = 49284

For detailed explanation check below:
https://www.hamaraguru.com/assets/files/2018-01-09/1515488080-867972-imgur-12.jpeg

\( 666^{2} \) = \( 6^{2} \) / 2\( (6^{2}) \) / 3\( (6^{2}) \) / 2\( (6^{2}) \) / \( 6^{2} \) = 36 / 72 / 108 / 72 / 36 = 443556

For detailed explanation check below:
https://www.hamaraguru.com/assets/files/2018-01-09/1515493637-503669-imgur-13.jpeg