Square of two digit number whose digits are same

Square of two digit number whose digits are same

Let us consider the 2-digit number as aa. Let’s see how the square of the number looks like:
https://www.hamaraguru.com/assets/files/2018-01-09/1515478099-68843-imgur-8.jpeg

Examples:
\( 11^{2} \) = \( 1^{2} \) / 2\( (1^{2}) \) / \( 1^{2} \) = 1 / 2 / 1=121

\( 22^{2} \) = \( 2^{2} \) / 2\( (2^{2}) \) / \( 2^{2} \) = 4 / 8 / 4=484

\( 55^{2} \) = \( 5^{2} \) / 2\( (5^{2}) \) / \( 5^{2} \) = 25 / 50 / 25=3025
For detailed explanation check below:
https://www.hamaraguru.com/assets/files/2018-01-09/1515481900-174350-imgur-9.jpeg

 

Similarly one more example:

\( 77^{2} \) = \( 7^{2} \) / 2\( (7^{2}) \) / \( 7^{2} \) = 49 / 98 / 49=5929
For detailed explanation check below:
https://www.hamaraguru.com/assets/files/2018-01-09/1515482367-273590-imgur-10.jpeg