Tricks and techniques to find square of a number with in seconds?

Solving aptitude and trying to do fast math?
you are here at the correct place then. this post enables you to solve square of a number within a few seconds when results are observed practically, the average time taken to find squares of 10 random numbers is 103 seconds.

Before going into the topic, let me tell my experience, it was a typical day in our college and that was a boring lecture and all the students were busy trying to listen the class, there begins the actual story my friend who is aiming to crack the CAT exam and get a seat in one of the reputed MBA school was doing some rough work at the end of his notes. he then told me the importance of fast math in the competitive exams and how it reduces the solving time from minutes to seconds in many cases. being curious about the fast math, I have searched a lot to find the squares of the numbers and found many techniques after watching youtube videos, referring some books, blogs... but it was a big question mark which one to believe and which method to avoid.
Then we have experimented with A/B strategy and practised to compute squares of more and more numbers with different techniques but tracking became the problem so I have written a program which displays the number and takes input from us then we have put together all the stats and found that the methods mentioned below are the best ones among all.

Isn't it cool to do such fast math?
let's move on to the topic,
There are 3 methods to find the square of a given number very fast out of which one can be applied to any number while the other two works fast only for a specific range.

Method 1: (numbers in the range 70-130)
  1. Find Diff=100-number
  2. [first two digits]: (Find number-Diff )
  3. [last 2 digits]: (square of Diff)
Example 75^2
Diff=100-75=25
[first two digits] 75-25(diff)=5000
Diff^2=25*25=625
5000+625 is the answer


Method 2: (numbers in the range 30-70)
  1. Find Diff=50-number
  2. [first two digits]: (25-Diff )
  3. [last 2 digits]: (square of Diff)
Example 51^2
Diff=50-51=-1
[first two digits] 25- (-1)(diff)=2600
Diff^2=(-1)^2=1
2600+1=2601 is the answer

Method 3: A^2 B^2 2AB method:
This method fits good with any number,
1)calculate A^2, B^2, 2*A*B
2)combine A^2, B^2
3)Add 2AB to above number leaving 1 space right extreme.

example:
71^2
A^2=7^2=49
B^2=1^2=01
2*A*B=2*1*7=14
now add both leaving 1 space at the right
4901
+14-
=5041

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Tool to calculate Square of a given number:

Hey M4APT, Tell me the square of


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comment here if you have any doubt or a new technique.

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