Fast Math Squaring Numbers Ending in 1

There are a couple of real nifty ways of doing fast math with numbers that end in 1.  We are going to present a addition method.  There are other methods that we will present in subsequent posts but this method presented is the easiest way to calculate squares ending in 1.  

Addition method:
Lets start with a number 71.

• We will subtract 1 from this number and call it our base number: 71-1=70
• We will square our base number: 70²=4900
• We will multiply our base number by 2: 70x2=140
• We will add the square of our base number to our base number multiplied by 20 and add 1.  4900+140+1=5041

That is pretty easy isn't it?

Lets find 101²
101-1=100

100²=10,000
2X100=200
10,000+200+1=10,201 

That is incredibly easy and fast!  Lets try one more number:

191²

191-1=190
190²=36100

2X190=380
36100+380+1=36481

Outstanding!  Now you know how to square numbers ending in one and you can do it very fast.  We will show how to do other numbers in subsequent posts so stay tuned.