# How to Quickly Calculate Square of Three Digit Numbers?

Learn to Quickly Calculate Square of Any Three Digit Number

The method of squaring any 3 digit number is an extension of my last post on finding square of any two digit number. To understand and appreciate squaring of 3 digit numbers you should be well versed with shortcut of squaring any 2 digit number. Let us start learning this with the help of an example.

What is the square of 384?

Step 1: To begin with ignore the 3 of 384. You are left with only 84, a two digit number. Using the method of squaring 2 digit numbers, find the square of 84. We get the answer as

Square of 8  |   twice of 8 X 4   |  square of 4

64            64           16

7056 (consolidating the result obtained above)

Step 2: This step is new and different from what we’ve learned in the previous post for squaring 2 digit numbers. Watch carefully.

We have to multiply the first and last digits of our original number and double it. Essentially, that is multiplying together 3 and 4 and then doubling it. Hence we get 24.

Add this number directly to the two left hand digits of our number obtained from the first step.

7056

Add 24 to 70. 70+24=94. So 7056 gets converted to 9456.

Step 3: In the first step we left out the first digit of our number and squared the last two digits. Now we will forget about the unit’s digit 4 and square the first two digits i.e. 38 as before just omitting to square the last digit 8.

Square 38 as a regular 2 digit number, except that you omit the 8 squared.

Square of 3 | twice of 3 X 8

9       |   48

Step 4: Consolidating this with the result obtained in step 2,

9   |  48   |  9456

14        7       456

I’ve shared this method of squaring 3 digit numbers as an extension to the shortcut of squaring 2 digit numbers. Initially you might feel that the traditional method is quicker than having to memorize and execute these steps. However, this method can prove to be quicker than the useful one only if you master this technique with lot of practice.

Do you think this method will help you in reducing the time to calculate square of 3 digit numbers?

#### Vineet Patawari

Hi, I'm Vineet Patawari. I fell in love with numbers after being scared of them for quite some time. Now, I'm here to make you feel comfortable with numbers and help you get rid of Math Phobia!

## 29 thoughts to “How to Quickly Calculate Square of Three Digit Numbers?”

1. yash says:

hey, admin are you serious ……do you think we have enough time in banking exam to solve this kind of Que by this method. according to me method is nice but too lengthy ….not working.

2. Sankar M says:

I checked out your example in that up to step 4 understood 9/48/9456 then how it was convert 14 7 456 please let u know .

3. NIRVIK says:

897*897 PLS DO THE SUM

1. akhil says:

hard not getting

2. akhil says:

hard not getting…..

3. akhil says:

i will show you another trick

89^2 double of 89×7 7^2
7921 1246 49

consolidate(mistakes happens while consolidating)

1st way 2nd way

4 9 + // 7 9 2 1
1 2 4 6 // 1 2 4 6
7 9 2 1 // 4 9
__________________________________________________
8 0 4 6 0 9 8 0 4 6 0 9

4. NIRVIK says:

PLS DO 897

5. R SRINIVAS says:

6. vasu says:

Hi Vineet,

1. Dear Vasu,

The above technique is to calculate SQUARE of 3 digit numbers. If you wish to calculate SQUARE ROOT of 4 digit numbers, please check these articles –

Hope that helps

Thanks
Vineet

7. yaminee says:

32.2^2 how to find decimal square . Pls help me using short trick
????

1. mohamed says:

first square 322 like he told you then ad the the ‘.’ befor the the fist 2 digit numbers like this
32.2 * 32.2 = 1036.84
and if it is 3.22*3.22
it will be
10.3684
and I apologize because of poor English

8. Sankar says:

Awesome tricks bro…can u pls upload some tricks for quantitative aptitude bro

9. Ronak Patel says:

Nice trick..

10. Mitchelle says:

Its great for 3 digit no’s, but I am finding it difficult for no’s with 0 in between like 105.

Please show me how to do for such no’s.

Thanks

11. ankit kumar says:

3 digit/2 digit short cut

12. upasna says:

Plz help me find square root of 4133 using above method

13. ashish says:

How to find square of decimals… such as -: 34.12^2

14. pavanteja says:

Does the square of 3 digit numbers valid for 219?

15. Mudit says:

how do we add 2*7*9=126 to left hand side digits of 89^2= 7921
same problem is encountered with many other 3 digit numbers- x,y,z
where 2xz is a 3 digit no. and x^2: 2 digit, 2xy
:3 digit. how do we consolidate the numbers in such a case?
example: for 789^2 i’m getting something like 49|112|20521(126+79)|21
Regards

1. 49|112|20521

= 49 | 112 + 20 | 521 (keep only 3 digits in right most part)
= 49 | 132 | 521
= 49+13 | 2 | 521

1. Mudit says:

Got it
Thanks sir!

16. MOHINI says:

sir pls help me find the square of 219 by the above method

17. ignore 7 in 742
so42
4 and 2 can be solved in this way

4^2|2*4*2|2^2

16|16|4

consolidating it

1764

multiply the first and last digits and double it

7*2*2=28

Add 28 in 17 of 1764

new no becomes 4564

now ignore 2 in 742
74

7 and 4 can be solved

7^2|7*4*2|4564

after consolidating

49|56|4564

we have 560564 an the answer

happy and enjoy [jitendra lakhara beru]

1. MOHINI says:

The answer has a typing mistake.it is 550,564.Please correct it, students get confused.

2. ajay says:

Dear ans will be 550564

18. sourav says:

ignore 8 in 863
so 63
6 and 3 can be solved in this way.

6^2 |2x6x3| 3^2

36 36 09

consolidating it
3969

Multiply the first and last digits and double it
8x 3×2 = 48

add 48 in 39 of 3969

new no becomes 8769

Now ignore 3 in 863
86

8 and 6 can be solved

8^2 |2x8x6| 8769

after consolidating

64 96 8769

we have 744769 an the answer.

enjoy!

19. yogapraba says:

sir can u help me in finding the square of 863 by using the above said method….pls hlp me sir

1. sourav says:

ignore 8 in 863
so 63
6 and 3 can be solved in this way.

6^2 |2x6x3| 3^2

36 36 09

consolidating it
3969

Multiply the first and last digits and double it
8x 3×2 = 48

add 48 in 39 of 3969

new no becomes 8769

Now ignore 3 in 863
86

8 and 6 can be solved

8^2 |2x8x6| 8769

after consolidating

64 96 8769

we have 744769 an the answer.

enjoy!