How to Do Speed Squaring Using Vedic Mathematics

Throw your calculator away. You wont be needing that after you read this.

You will not believe until you try it out.

Many might have heard about the ancient Indian mathematical techniques better known as Vedic mathematics. It is a very vast subject in itself. Many of the techniques described in Vedic mathematical techniques are far simpler and faster than the conventional methods. The best part is you can do even the most complex calculations in your mind using these techniques.

How good are you at finding squares of numbers? I bet most of the people would know squares up to 10. But what will happen if you are given a number after 30? Ok, let us make it a little more tough, who can find the square of 991 in 5 seconds? Don’t run for pen and paper, just read through.

I just wanted to introduce you to a technique which I like the most. This technique is used to find the square of a big number. I will take a few examples and try to describe the technique here. Here are the steps you should do to find the square of a number according to Vedic mathematics. I have taken two example numbers – 109 and 991

Step 1

Subtract the nearest power of 10 from the number. So, if you are thinking about 109, the result of step 1 will be 109 – 100 = 9. If you are taking the number 991, the result will be negative. I.e. the result will be 991 – 1000 = -9.

Step 2

Add result of step 1 to the original number. So, in the first example above, the result will be 118 and for the second example the result will be 982.

Step 3

Find the square of result from step 1. So in the first and the second example, the result will be 9 * 9 = 81.

Step 4

Combine the results of step 2 and step 3 after padding enough zeroes if required. So, the answer to the fist example 109 * 109 will be 11881 and the second example 991 * 991 will be 982081

Yes, go on, take your calculator and check out the results.

Extension of the above technique

This technique works very well if the number you have selected is nearer to the power of hundred like 10,100,1000,10000 etc. But what if the number you selected does not fit that criteria. We can extend this technique to fit our requirement. But in this case you should be able to do small amount of multiplication also.

For example let us take the number 73. If we have to apply this technique, then you should know the square of 27 which I bet 50% of the people will not remember. So, the easy way to apply this technique is to find the nearest multiple of 10 which in this case is 70. So, following step 1 we will get 73 -70 = 3. Following step 2 we will get 73 + 3 = 76. Now comes the tricky part. We have to multiply 76 with the multiple of 10 which we used as base which in this case is 7. So 76 * 7 = 532 (If you find it difficult to multiply just break it down and think 76*7 = (70*7) + (6*7) and you will get the answer as 532)

Now follow step 3. 3 * 3 = 9. And finally to step 4, we will get 5329.

This is just one among the hundreds of methods used in Vedic Mathematics. This technique can be expanded as above to find bigger numbers. But I am not going to spoon feed everything. Try to think about it and keep your brain alive. Throw that calculator away to have a healthy brain.

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8 Responses to “How to Do Speed Squaring Using Vedic Mathematics”
  1. Darren Says...

    On January 17, 2008 at 4:47 am

    Very interesting. Would be good if you can post more such articles.

  2. Friedman Says...

    On February 17, 2008 at 11:29 pm

    That’s fantastic. I never knew that we have a technique like this. Where can i find more information about these kind of techniques?

  3. saksham Says...

    On November 10, 2008 at 3:58 am

    a nice and effective technique for a complex task

  4. Ori Sonata Says...

    On February 26, 2009 at 10:42 am

    Good article. However I still need my calculator for calculating something like (6.332+4.343i)^3.21, so I can’t really throw it :)

  5. Shubham Says...

    On May 17, 2009 at 1:21 pm


  6. mrigank tiwari Says...

    On May 18, 2009 at 10:52 am

    quite intresting ,mind blowing technique it is ,really cool.

  7. K V Venkataramana Says...

    On October 16, 2010 at 10:52 pm

    Really astonishing.

  8. anuar Says...

    On January 27, 2011 at 11:10 am

    nice article…should be more fantastic…

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