How to Square Numbers Quickly

In this post we are going to look at how to square any two digit numbers.
[private]Firstly, to square a number means to multiply that number by itself.

So 27² means 27 X 27

When squaring any number we need to either work up or work down from a BASE number. We acknowledge that a base number is a whole number closest to the number we want to multiply. So taking the above example of 27² we would use the base number of 30.

So, the first rule we need to do is find the base number.

Next rule, we need to count how far away the number to be squared is from the base.

Keeping with the above example, we know that 27 is three away from 30.
So now we lay out the calculation like so:Squaring numbers quickly

As you can see, we’ve also added 24 to the image. You see, when we add three to the 27 to get 30, we also need to take 3 away from 27 to balance the sum.

You would do this for all sums you are squaring using this method.

The next step is real simple We need to multiply 24 X 30… Don’t worry! It’s easy and here’s why.

We don’t really need to multiply 30 X 24 or 24 X 30 (same thing), all we need to do is multiply 24 X 3 and then add a 0 to the end.

I would probably do 24 X 3 this way:

Add one to 24 giving 25, then 25 X 3 = 75.

Take away the three 1’s giving us 72.
So 24 X 3 = 72
Now we can add back the 0 and we find that 24 X 30 = 720.
The sum is almost complete.

Look back at the image again:

How to square numbers really quickly

Notice the +3 and -3. Forget about any – values and just multiply 3 X 3 giving 9.

Add this to 720 and we find that

27² = 729

Don’t get overwhelmed by it from that one example. It really is a pussycat once you’ve grasped how to do it

Let’s try another example, and this time it’s going to be an even bigger number than before, but it certainly doesn’t make it any more difficult.

Let’s say 56²

Lay out the sum again just like in the image before:Squaring 56 squared quickly

So, just like before we need to multiply 52 X 60 but all we really need to do here is multiply 52 X 6 and add a 0 on the end.

52 X 6 is easier if you do 50 X 6 which is 300 then 2 X 6 = 12 so

52 X 6 = 312
Add the 0 on the end and 52 X 60 = 3120

Take the +4 and -4 and just multiply the numbers 4 X 4 giving 16. Add it to the end of 3120 and we get

56² = 3136

By using this technique I hope you can see that those big calculations aren’t that difficult once you have a good system in place.[/private]

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23 Responses to “How to Square Numbers Quickly”

  1. I never ever post but this time I will,Thanks alot for the great blog.

  2. its just fantabuolous….

  3. very nice.

  4. i liked it very much
    it's amgzing.


  6. I have five squares numbered 1, 2, 3, 4, 5. How many combinations of 3 squares can I make?

  7. 2*2=4

  8. it is a very amgzing. i like that.

  9. Where can i watch the old 2002 show Mentors? ):?

  10. Long Term / Short term memory problem when trying to recall technical info?

  11. i want 2 learn vedic maths. where to go? is it effective?????

  12. really its a good technical and u r doing a lot

  13. Please elaborate the same for n digit number.. thanks!

  14. Um… This didn't work for 29! So confused!

  15. I got 840 using your method and my calculator says that it is 841!

  16. cooooooooooooooooool…it works for every number….even 29

  17. tell ne quick way to square any 3 digit number

  18. this is really good it totally works………………..

  19. this method is a wonderful method of squaring number

  20. Your have to add 1 in last . I thing you forgot that term.

  21. I thing the cross multiplication is more easy than this method.

  22. Dude, I have one more method though i liked this one too…
    My method is ==>Lets say u wanna find the square of the number 23
    23^2 can be written as
    2 | 3 ==> We separate the digits
    4 9 (Here we square the individual digits….)
    1 2 (Multiply both the digits and then multiply the
    product by 2 i.e., 2*(2*3)=12, write the 2 in the
    middle and 1 below 4 and then add them… )
    5 2 9

    If we have say 69 then ==>
    6 | 9
    3 6 8 1 (6^2 = 36 and 9^2 = 81)
    1 0 8 (2*(6*9) = 108)
    4 7 6 1 ==> that’s the answer

    Though the already given is greaaaattttt….. :)

  23. thanks for sharing this tricks with us…………

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