Finding Square of an adjacent number:

Finding Square of an adjacent number: One up

You know the squares of 30, 40, 50, 60 etc. but if you are required to calculate square of 31 or say 61 then you will scribble on paper and try to answer the question. Can it be done mentally? Some of you will say may be and some of you will say may not be. But if I give you a formula then all of you will say, yes! it can be. What is that formula…..

The formula is simple and the application is simpler.

Say you know 60² = 3600

Then 61² will be given by the following

61² = 60² + (60 + 61) = 3600 + 121 = 3721

or Say you know 25² = 625 then

26² = 625 + (25 + 26) = 676

Finding Square of an adjacent number: One below

Likewise, you can find out square of a number that is one less than the number whose square is known.

Let me show it by taking an example:
Say you know 60² = 3600
Then 59² will be given by the following
59² = 60² – (60 + 59) = 3600 – 119 = 3481
or Say you know 25² = 625 then
24² = 625 – (25 + 24) = 576
Apply it to find square of a digit, which is one, less than the square of known digit. This works very well for the complete range of numbers.

Finding Square of a number ending with 5

After learning this you will be able to find square of a number ending with 5 say 25, 35, 45 etc. You can even try to find square of a three digit number ending with 5 say 105, 115, 125 etc.
Say you want to find square of 85
Do the following:
· Multiply 5 by 5 and put 25 as your right part of the answer.
· Multiply 8 by the next higher digit i.e 9 and put 72 as your left part of the answer.
· Your answer is 7225
You can use this formula to find square of any number ending with 5.

More details can be found at Magical Methods