Squaring 3 digit numbers ending in 1

There is a short cut method for squaring 3 digit numbers ending in 1 rather than going for normal multiplication. If you can practice a bit with this method then you can square such numbers in mind itself. Let me explain the method with an example.

Squaring of 3 digit numbers ending in 5

Let me explain the easier method for squaring 3 digit numbers ending in 5 with an example:

Squaring Numbers ending in 9

Squaring Numbers ending in 9
To square numbers ending in 9 like 19, 29, 39, 49....you know square of 9 is 9 x 9= 81, you can use this for speedy calculation. Now to the technique let me explain with example

1^st example 19²

step 1 : Add 1 to the number so that the number will be ending in 0
             19+1 =20
step 2 : find square of it as it ends in zero finding its square is easy.
              20²  = 400
step 3 : Add the 19 to 20
              19 + 20 = 39
step 4 : subtract the result of step 3 from resutl of step 2 and that will be your answer
              400 - 39= 361
              thus 19²  = 361

2^nd example 79²

step1 : 79+1 =80

step2 : 80²  = 6400

step3 : 79+80 =159

step4 : 6400-159=6241

thus 79²  = 6241

Squaring Numbers ending in 5

Squaring Numbers ending in 5
To square numbers ending in 5 like 15, 25, 35, 45....you know square of 5 is 5 x 5 = 25, you can use this for speedy calculation. Now to the technique let me explain with example

1^st example 15²

step 1 : Separate digit 5 from the number 15 then the remaining digit is 1
step 2 : add 1 to the remaining digit(s) here
              1 +1 = 2
step 3 : Multiply the number from step 1 and step 2
              1 x 2 = 2
step 4 : write 5² ie 25 after the result of step 3 ie 225
              thus 15²  = 225

2^nd example 95²

step1 : seperating 5 the remainng digit is 9

step2 : 9 +1 =10

step3 : 9 x 10 = 90

step4 : 95²=9025

Squaring Numbers ending in 3

Squaring Numbers ending in 3
To square the numbers ending in 3like 13, 23,33, 43..upto 93. there is an easy method let me explain with an example.

1^st example 13²

step 1 : Split the 2 digits of the number and square each digit to make the ones' place and 100th place respectively of the square
1²=1
3²=9
step 2 : multiply the tens digit of the number to be squared to 6 and it will be the tens digit of the square
here 1x4 =4
1 9
 6
---------
169
---------
so the square of 13 is 169.

2^nd example 43²
step 1 : Split the 2 digits of the number and square each digit to make the ones' place and 100th place respectively of the square
4²=16
3²=9
step 2 : multiply the tens digit of the number to be squared to 6 and it will be the tens digit of the square
here 4x6 =24
16  9
  24
-------------
1849
-------------
so 43²=1849

Squaring Numbers ending in 2

Squaring Numbers ending in 2
To square the numbers ending in 2 like 12, 22,32, 42 .upto 92. there is an easy method let me explain with an example.

1^st example 12²

step 1 : Split the 2 digits of the number and square each digit to make the ones' place and 100th place respectively of the square
1²=1
2²=4
step 2 : multiply the tens digit of the number to be squared to 4 and it will be the tens digit of the square
here 1x4 =4
1 4 +
  4
---------
144
---------
so the square of 12 is 144.

2^nd example 42²
step 1 : Split the 2 digits of the number and square each digit to make the ones' place and 100th place respectively of the square
4²=16
2²=4
step 2 : multiply the tens digit of the number to be squared to 4 and it will be the tens digit of the square
here 4x4 =16
16  4+
  16
-------------
1764
-------------
so 42²=1764

SQUARING numbers ending in 4

Squaring Numbers ending in 4
To square the numbers ending in 4 like 14, 24,34, 44..upto 94. there is an easy method let me explain with an example.


1^st example 14²


step 1 : Split the 2 digits of the number and square each digit to make the ones' place and 100th place respectively of the square
1²=1
4²=16
step 2 : multiply the tens digit of the number to be squared to 8 and it will be the tens digit of the square
here 1x8 =8
1 16
   8
---------
196
---------
so the square of 14 is 196.

2^nd example 44²

step 1 : Split the 2 digits of the number and square each digit to make the ones' place and 100th place respectively of the square
4²=16
4²=16

step 2 : multiply the tens digit of the number to be squared to 8 and it will be the tens digit of the square
here 4x8 =32
1616
  32
-------------
1936
-------------
so 44²=1936

SQUARES of numbers ending in 1

What do you mean by squaring a number?
Squaring means multiplying a number by itself.
example: squaring 3 means 3 multiplied by 3 (3x3) it will be written as 3² =9
Now lets move on to the funda..
Quick mental calculations can help in solving problems faster and practice of this can become a gift
We can find the squares using some technique this will help find the squares faster.

Squaring Numbers ending in 1

This is the short cut method to find out squares of numbers ending in 1 like 11,21,31,41,121,131 etc if we go for multiplying the numbers it will take longer time

1^st example 21²

step 1 :  subtact 1 from the number, so that the number ends in zero.
                       21-1=20
step 2 : find the square of the difference, its easy to square numbers ending with 0.
                       20² = 20x20 = 400
step 3 : add the number we now squared ie 20 and to the number to be squared ie 21
                       20+21=41
step 4 :add the result of step 2 to step 3 this will give you the answer of 21²
                       400 + 41 =441.
so 21² =441.

2^nd example 41²

step 1 : 41 - 1= 40

step 2 : 40² =40 x 40 = 1600

step 3 :40 + 41 = 81

step 4 : 1600 + 81 = 1681

so 41² =1681