## 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 digit number, 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 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**

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

###

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

###

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

##

####

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

##

The square of 78 is 6084

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

###

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

####

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

Here 8*8=64+9=73, 7 at 1st digit and 3 at 2nd digit

####

The square of 86 is 7396

To learn one more maths tricks

To find square of 135

when unit place of a number ends with 5

then place 25 as last two digits (i. e right most ) of the result

####

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

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 .

##

##

- - - - -

1st 2nd 3rd 4th 5th

###

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

####

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

####

The square of 132 is 17424.

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

###

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

####

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.

####

The square of 146 is 21316

###

Step 2 Multiply 2*12*7 =168 , Add carry of 4 to it and get 168 + 4 = 172, write

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

###

Step 2 Multiply 2*25*7 = 350 , Add carry of 4 to it and get 350 + 4 = 354 , write

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

**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.##
**78**^{2 }^{ }= ^{ ??}

^{2 }

^{ }=

^{ ??}

^{1st Step Make square of unit place .i.e. }**8**

^{2 }^{ }= 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 .

## Last Step

**Write square of ten's place =**

^{ }**7**9

^{2 }^{ }= 4

**+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.

####
**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 1The 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.

####
**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**

## Final Words

Thanks for spending your precious time to this post of multiplication tricks, finding square of two and three digits numbers quickly , If you really gained something from this post ,then Share this post with your near and dear , Also follow me on my blog . We shall meet again in next post , till then Good Bye.

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