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 = 502 + 2 x 50 x a + a2 = 2500 + 100a + a2 = 100(25+a) + a2 = (25+a) / a2
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 52 + 6 to get 31. This forms the 1st part of the answer.
So, 562 = 3136
One more Example: