What is the best short-cut trick to find the square of any number between 10 to 99?
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This method as below is the easiest and fastest way to find the square of any number less than 100.
Example 1: Suppose you want to find the square of 56. That is we want to find the value of 56 * 56 (562) in a quick way.
what we can do is first we can denote the first digit by 'a' and 2nd digit by 'b' in the number 56.
a = 5
b = 6
then we need to apply this formula
a2 | 2ab | b2
52 | 2 * 5 * 6 | 62
25 | 60 | 36
But in the third and right-most column, we will write only 6 (2nd digit of 36) and carry 3 (first digit of 36) to be added to 60 (the value in the 2nd and middle column). Now the value becomes 63 in the middle column but we will write only 3 (of 63) and carry 6 to be finally added to 25 (the value in the first column). The end result will look like this.
31 | 3 | 6
After removing vertical dashes the answer will be 3136.
Example 2: Suppose you want to find the square of 93. That is we want to find the value of 93 * 93 (932) in a quick way.
Just we can do the calculation in the mind and no need to write the formula in a piece of paper. Just be aware of the formula in the mind.
In 93, first multiple the 2nd digit by itself that is 3*3 = 9 (there is no carry as the value is less than 10).
this 9 is the last digit of the final answer (consider this as note 1 value).
Now in 93, multiply the two digits (9 and 3) by 2 to get the value 54. But we will write only 4 (consider this as note 2 value) from 54 and carry 5 to be added to the square of the first digit > 9 in the value 93.
So 81+5= 86 (consider this as note 3 value).
So, the final answer will be grouping of note 3 value - note 2 value- note 1 value
which will be 8649 (the final answer).
Example 3: Suppose you want to find the square of 78. That is we want to find the value of 78 * 78 (782) in a quick way.
In 78, first multiple the 2nd digit by itself that is 8 * 8 = 64. In this 64 value, we will only write 4 (2nd digit of 64) and carry 6.
So, 4 (consider this as note 1 value with a carry of 6).
Then in 78 we will multiply the two digits (7 and 8) with each other and then with 2 as below.
2 * 7 * 8 = 112 (but we will write only 2 (last digit of 112) and carry 11).
So 2 + (carry from note 1) (here we also added carry from note 1 above)
So 2 + 6 = 8 (consider this as note 2 value + carry of 11 from above)
Finally we will square 7 (in 78) to get 49 (+ carry 11 from note 2) = 60
So 60 (consider this as the value of note 3).
The final answer will be the note sequence as below
note 3 value - note 2 value - note 1 value
6084 (this is the final answer).
Hope it makes sense and it is clear.
You can test it and it works for all numbers from 10 to 99.
Here is the easiest method to find the square of any 3-digit numbers using another formula.
But there is also a great method to find the square of any number without using the formula but still very quickly.
There is also one universal method to find the square of any number without worrying whether it is a 2-digit, 3-digit, 4-digit or 5-digit number and it is the easiest and fastest method of all.
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Written by: Rajesh Bihani ( Find me on Google+ )