Square of a number which lies between 51 and 59

Square of a number which lies between 51 and 59

Proof: Any number from 51 to 59 can be represented as (50 + a). Taking the square of this number we have equation as:

\( (50+a)^{2} \) = \( 50^{2} \) + 2 \( \times \) 50 \( \times \) a + \( a^{2} \) = 2500 + 100a + \( a^{2} \) = 100(25+a) + \( a^{2} \) = (25+a) / \( a^{2} \)
https://www.hamaraguru.com/assets/files/2018-01-12/1515740148-782492-imgur-24.jpeg
Steps for better understand:
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 right side. Obtain the square of 6 to get 36. This forms the 2nd part of the answer.
Step 3: You have 5 on the left side. Take the square of it and add the number on the right side, that is \(5^2\) + 6 to get 31. This forms the 1st part of the answer.
So, \( 56^{2} \) = 3136

One more Example:
https://www.hamaraguru.com/assets/files/2018-01-12/1515740541-780111-imgur-25.jpeg