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

Hence the answer is 147456.

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. 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. 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 .

    1. 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

    1. 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
      I hope this help you
      and I apologize because of poor English

  3. 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

  4. Sir what about 789^2 ?
    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

  5. 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]

  6. 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!

    1. 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!

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