### Squaring of a number ending with 1 (one)

This technique works well for squaring number ending with 1. If you multiply the numbers the traditional way you will see why this works.

For example:

**31**^{2 }=

Firstly, subtract 1 from the number. The number now ends in zero and will be quite easy to square now.

**30**^{2 }= **900** (3 x 3 x 10 x 10)

This is our sub-total.

Secondly, add together 30 and 31 -- the number we squared plus the number we want to square.

**30 + 31** = **61**

Add this to our sub-total, 900, to get **961** (900 + 61) , which becomes the answer.

__Note:__ For the second step you can simply __double the number we squared, 30 x 2 and then add 1.__

Another example is:

**121**^{2 }=

**121 - 1** = **120**

**120**^{2 }= **14400** (12 x 12 x 10 x 10)

**120 + 121 = 241**

** 14400 + 241 = 14641 [ Answer]**

__Self Exercises__:-a) 21

^{2}=

b) 41

^{2}=

c) 81

^{2}=

d) 141

^{2}=

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