Square of a Number ending with 05

Square of a Number ending with 05

Let’s say, we want to calculate the square of \( 205^{2} \) . The entire steps are illustrated in the following figure.
https://www.hamaraguru.com/assets/files/2018-01-12/1515756149-624941-imgur-36.jpeg
Steps for better understanding:
Step 1 : Break the number such that 05 is on the right and the rest of the digits is on the left.
Step 2 : Obtain the square of 05 on the right to get 025. This forms the second part of the answer. A number ending with 05 will always have 025 as the 2nd part of the answer when we take its square.
Step 3 : Take the rest of the digits(2) and take its square followed by the digit itself which forms the 1st part of the answer.
So, \( 205^{2} \) = \( 2^{2} \) / 2 / 025 = 42025.

Few more Examples:
https://www.hamaraguru.com/assets/files/2018-01-12/1515757356-352802-imgur-37.jpeg
https://www.hamaraguru.com/assets/files/2018-01-12/1515757360-204815-imgur-38.jpeg

Notice the difference from the previous example. In this case, we have 2-digits on the left. So, we need to consider the carry – over.

So, \( 1205^{2} \) = \( 12^{2} \) / 12 /025 = 144+1/2/025 = 1452025