SHORTCUT TO FIND THE SQUARE OF A 3 DIGIT NUMBER, VEDIC MATHS SQUARE OF TWO DIGIT NUMBERS

We shall learn a shortcut to find square of a 3 digits numbers , vedic maths square of two digit numbers, i. e. how to find square of any number, This method is very much time shaving and easy.

Square of Two And Three Digits Numbers

 

In order to save time  in computing long arithmetic  calculations ,sometime we need short cuts which are effective to save time and easy to understand. There are many shortcuts available to compute faster ,one of them is discussed below with the help of Examples .

Example :   To Find the Square of Two Digits Numbers Ending with 5

Here I shall show  how square of 35 can be  found quickly.

Step 1 

when unit/(Right most)  place of a number ends with 5 
then place 25 as last two digits (i. e Right most ) of the result.

Step 2 

Take the digit which is on the unit's place and multiply it with its successor (next digit from it), Here in this case the 1st two digits are 12, the product of 3 and its  successor 4. 

Step 3

The result will be  four digit numbers whose first two digits are answer  of step 2 and next two digits are answer of step 1

The square of  35 = (3*4)(25)
                                        = 1225

Example

To find Square of   65

1  Place 25 as last two digits of the answer as given number ends with 5

2 Place the product of  6 and it successor i.e. 7 which is equal to 42

So Answer will be   4225

Hence
Square of 55 is (5*6)  = 30  as 1st two digits (25) as last two digits = 3025

Square of 75 is (7*8)  = 56  as 1st two digits(25) as last two digits = 5625

Square of 45 is (4*5) =  20 as 1st two digits (20) as last two digits = 2025

Square of 25 is (2*3) = 06 as 1st two digits (25) as last two digits = 625

Square of 85 is (8*9) = 72 as 1st two digits (25) as last two digits = 7225

2nd Example : To find the Square of  two digits number not ending with 5

Here  we are taking example of  78,  the digit in unit's place is 8 and the digit in ten's place is 8, result of square of any two digits number will be written in four digits .

               -          -         -        -
         1st     2nd      3rd    4th

Step 1 

Square  unit  place's digit if it is two digits number then write units place digits in 4th place and reserve the ten place 's digit for next step , Here square of 8 is 64 so write 4 at 4th digits in answer and reserve 6 as carry forward  for next step.

8*8 = 64, 4 as 4th place  and 6 as carry forward

78²    =  ^??

^{1st Step Make square of unit place .i.e.}   8²    = 64

Write  4 as unit place of answer and carry forwarded 6 to 2nd step

Step 2

          Now multiply both the digits of our example and then again multiply it with 2 and add carry forwarded number of the step 1 to it, write the extreme right digit of the result so obtained in place of 3rd place, and reserve the remaining digit/digits as carry forward for next step.

Here 2×7×8=112 + 6 = 118 , 8 at 3rd place and 11 as carry forward for next step.

2nd Step

Calculate 2×7×8 = 112+(6 carry forwarded) = 118

write 8 as Ten's Place in answer and carry forward 11 to next step

Step 3

        Take the square of  ten's place digit and add  the carry forwarded result from previous step and place on 1st and 2nd place.

 Here 7×7 = 49 + 11 = 60,  6 at 1st digit and 0 at 2nd digit .

The square of 78 is 6084

Last Step 

Write square of ten's place =   7²    = 49 +11 = 60

So Final Answer will be  6084

3rd Example : To find the Square of  two digits number not ending with 5

Here  we are taking example of  86, here in unit's place is 6 and in ten's place is 8,result of square of any two digits number will be written in four digits .

               -          -         -        -
         1st     2nd      3rd    4th

Step 1 

         Take the Square of  unit  place's digit if it is two digits number then write units place digits in 4th place and reserve the ten place 's digit for next step , Here square of 6 is 36 so write 6 at 4th digits in answer and reserve 3 as carry forward  for next step.

6×6=36, 6 as 4th place  and 3 as carry forward

Step 2

          Now multiply both the digits of our example and then again multiply it with 2 and add carry forwarded digit of the step 1 to it, write the extreme right digit of the result so obtained in place of 3rd place, and reserve the remaining digit/digits as carry forward for next step.

Here 2*8*6=96+3=96 , 6 at 3rd place and 9 as carry forward for next step.

Step 3

        Take the square of  ten's place digit and add  the carry forwaded result from previous step and place on 1st and 2nd place.
 Here 8*8=64+9=73, 7 at 1st digit and 3 at 2nd digit

Step 4

The square of 86 is 7396

To learn one more maths tricks

Example :   To Find the Square of Three Digits Numbers Ending with 5

Split this three digits number into two number , right extreme number as unit place and remaining two digits as Ten's place (assumed as one digit).

To find square of 135

step 1 

when unit place of a number ends with 5 
then place 25 as last two digits (i. e right most ) of the result

Step 2 

Take the digits which is on the unit's place and multiply it with its successor (next digit from it), here in this case the  product of 13 and its  successor 14 is equal to 182

Step 3

The result will be  five digit numbers whose three digits are answer  of step 2 and next two digits are answer of step 1

The square of 135 = (13×14)(25) = 18225

 So here is the multiplication tricks and short cut method to find the  Square of two and three digits numbers  .

2nd Example : To Find the Square of Three Digits Number Not Ending with 5

Now we are taking example of  132, here  unit's place is 2 and  ten's place is 13 (only assumption) ,result of square of any two digits number will be written in five digits .

               -          -         -        -     -
         1st     2nd      3rd    4th   5th

Step 1 

        Find  Square of  unit place's digit if it is two digits number then write units place digits in 4th place and reserve the ten place 's digit for next step , So  square of 2 is 4 therefore  write 4 at 5th digits in answer and reserve 0 as carry forward  for next step.

2*2=4, 4 as 5th place  and 0 as carry forward

Step 2

          Now multiply both the remaining digits of our example and then again multiply it with 2 and add carry forwarded digit of the step 1 to it, write the extreme right digit of the result so obtained in place of 4th place, and reserve the remaining digit/digits as carry forward for next step.

Here 2*13*2=52+0=52 , 2 at 4th  place and 5 as carry forward for next step.

Step 3

        Take the square of  ten's place digit (assumed 13) and add  the carry forwarded result from previous step and place on 1st , 2nd and 3rd  places.

Here 13*13=169+5=174, 1 as 1st digit , 7 as 2nd digit and 4 as 3rd digit  

step 4

The square of   132 is   17424.



             

3rd Example : To Find the Square of Three Digits Number Not Ending with 5

Here  we are taking example of  146, here  unit's place is 2 and  ten's place is 14 (only assumption) ,result of square of any two digits number will be written in four digits .

               -          -         -        -     -
         1st     2nd      3rd    4th   5th

Step 1 

Find  Square  of unit  place's digit if it is two digits number then write units place digits in 4th place and reserve the ten place 's digit for next step , Here square of 6 is 36 so write 6 at 5th digits in answer and reserve 3 as carry forward  for next step.

6*6 = 36, 6 as 5th place  and 3 as carry forward

Step 2

          Now multiply both the remaining digits of our example and then again multiply it with 2 and add carry forwarded digit of the step 1 to it, write the extreme right digit of the result so obtained in place of 4th place, and reserve the remaining digit/digits as carry forward for next step.

Here 2*14*6 = 168 + 3 = 171 ,   1 at 4th  place and 17 as carry forward for next step.

Step 3

        Take the square of  ten's place digit (assumed 13) and add  the carry forwarded result from previous step and place on 1st ,2nd and 3rd  places.

 Therefore  14*14 = 196 + 17=213, 2 as 1st digit , 1 as 2nd digit and 3 as 3rd digit  

step 4

The square of   146 is   21316

To Find The square of the Number 127

Step 1   Square of 7 =49 write 9 at unit place and carry 4 to next step.

Step 2    Multiply 2*12*7 =168 , Add carry of 4 to it and get  168 + 4 = 172, write 2  at hundred place and carry 17 to last step

Step 3 Add 17 to the  Square of 12 i.e  144  like this 144+17  = 161,
write 161 as 1st three digits of the answer
So the Answer is 16129

To Find The square of the Number 257

Step 1   Square of 7 = 49 write 9 at unit place and carry 4 to next step.

Step 2    Multiply 2*25*7  = 350 , Add carry of 4 to it and get  350 + 4 = 354 , write 4  at hundred place and carry 35 to last step

Step 3 Add 35 to the  Square of 25 i.e  625  like this 625 + 35  = 660,

write 660 as 1st three digits of the answer


So the Answer is 66049

Also Read This >>>You Know How to Multiply Fast 

                                        

Final Words

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