You probably already know the shortcut “how to obtain the square of any 2 digit number”. In this shortcut, will try to understand the shortcut how to obtain the squares of the numbers from 51 to 59. Even though, you can use the shortcut “how to obtain the square of any 2 digit number” for numbers from 51 to 59, you will see this shortcut will be much faster if you have to obtain the square of the number from 51 to 59.
Mathematical Proof for Squares of the numbers from 51 to 59
Let us understand the algebraic proof behind this shortcut.
Any number from 50 to 59 can be represented as (50+a). Taking the square of this number we have,
The squares of any 2-digit number would be of the form (25+a)/a2.
Let’s say, we want to obtain the square of 56. The entire steps can be illustrated in the following figure.
Step 1: First step is to break the number such that you have 6 on the right and 5 on the left side.
Step 2: Obtain the square of the digit on the right. So, we have 6 on the RHS. Obtain the square of 6 to get 36. This forms the RHS part of the answer.
Step 3: You have 5 on the LHS. Take the square of it and add the number on the RHS, that is 52 + 6 to get 31. This forms the LHS part of the answer.
Let’s consider another example. Can you mentally calculate the square of 59. The steps are illustrated in the following figure.
Using this technique, can you obtain the square of:
If you have any queries regarding this tutorial, please leave a comment. I would be glad to help