Squaring numbers ending in 1

Here’s a simple trick to square any number that ends in 1.

• Subtract 1 from the number.
• Square the difference. (Squaring of such number is easy as it ends in ‘0’)
• Add the difference twice to its square.
• Add 1.

Example: If the number to be squared is 61  

1.    Subtract 1=> 61 - 1 = 60.

2.    Square the difference => 60 × 60 = 3600.

3.    Add the difference twice to its square => 3600 + 60 + 60 = 3720.

4.    Add 1 => 3720 + 1 = 3721.

So, 61² = 3721

81² =?

1)    81 - 1 = 80 (Subtract 1). 

2)    80² = 6400 (square the difference). 

3)    6400 + 80 + 80 = 6560 (add the difference twice to its square).

4)    6560 + 1 = 6561 (add 1)

So, 81² = 6561

If the number to be squared is a 3-digit number, let’s say 121

1)    121 - 1 = 120 (Subtract 1). 

2)    120² = 14400 (square the difference). 

3)    14400 + 120 + 120 = 14640 (add the difference twice to its square).

4)    14640 + 1 = 14641 (add 1)

So, 121² = 14641

251² =?

1)    251 - 1 = 250  

2)    250² = 62500 

3)    62500 + 250 + 250 = 63000

4)    63000 + 1 = 63001

So, 251² = 63001

Ref. http://faster-maths.blogspot.com/2013/05/squaring-numbers-ending-in-1.html#.UadByNjKWVo