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Finding the cube root of a number by the traditional method is time consuming but by using simple Vedic maths trick "mere observation", we can find the cube root of any number within 2 to 3 seconds.

We all know the 27 is the cube of 3 and cube root of 3 is 27 which means the reciprocal procedure of calculating the cube is the cube root. Though this sounds easy, the procedure to find cube root for bigger numbers like  421,875 becomes a quite tricky and time consuming. For such bigger numbers, we can find the cube root in as 2 to 3 seconds by just looking at the number with perfect practice.

Proceeding further, lets make sure we know  the following two rules mentally.

Rule 1 : Know the cubes of first 10 natural numbers

cube roots trick

Rule 2:  Last digit of cube roots

cube roots

General Instructions for mere observation

  1. Divide the number into two groups as L.H.S and R.H.S by putting a slash 3 digits from the right
  2. Use rule 1 for L.H.S and find the cube root closer to that number.
  3. Use rule 2 for R.H.S and find the last digit of the cube root.

Lets start with an example say, find the cube root for 32768?

cube roots easy

1. Divide the number into two groups by putting a comma or slash after 3 digits from the right.
    32 | 768 

2. By observing the L.H.S of the number 32 and taking the perfect cube smaller than 32, we can conclude that square root of the number should be 3 from rule 1. Hence for our first digit on L.H.S, the cube root is 3.     32 | 768 
     3 

3. Coming to the R.H.S, we have 768 as our number. And from rule 2, we know that when the last digit of the cube is 8, its cube root should be 2. Therefore, our R.H.S of the cube root is 2. 
    32 | 768 
     3      2

Therefore, we have successfully found that the cube root for 32768 is 32.

Another Example,

Now lets find the cube root for 421,875.

Cube root for 421, 875 = 421 | 875
                                     =  7   |  5  
Therefore cube root for 421, 875 is 75. We found our answer just in seconds by following mere observation rule.

Now try finding the cube root for the following,
  1. 79507
  2. 592704
  3. 1157625
Note:  This technique only works for perfect cubes and will not work for any arbitrary n-digit numbers.



22 comments:

  1. This is excellent. Can you pls refer me a book to learn vedic maths.

    ReplyDelete
  2. Wow! Explained in a simple manner.

    ReplyDelete
  3. Wow Ums, good going, love your interest in Vedic maths :)

    ReplyDelete
  4. This is really wonderful. I will teach this now to my students. Thanks a lot Uma and an amazing job

    ReplyDelete
    Replies
    1. Sure Ritesh! Students can always gain from knowing different ways and methods to tackle maths :)

      Delete
    2. It's an awesome way to find cube roots of perfect cubes, but wat about non-perfect cubes?

      Delete
  5. Excellent and interesting. How can we divide large numbers?

    ReplyDelete
    Replies
    1. Hi Ruda,
      Good question. For numbers up to 7 digits , you can use the above rules and tips.
      If you wish to proceed further adding more digits say about 10 to 15 digits, you easily do so by extending Rule 1 by knowing the cubes of first 15 or 20 natural numbers.
      Cheers!

      Delete
  6. Anonymous10 May, 2014

    Going to take me practice but thank you !

    ReplyDelete
  7. i did not understand that in rule one we have to put the number closer to the cuberoot or nera to the perfect square

    ReplyDelete
    Replies
    1. In Rule one, the number closer to the cube is what we should use. In above example, L.H.S number 32 is closer to the number 27 and hence we took number as 3.

      Delete
  8. Hi I am a visitor of this site. Can you please solve a seven digit number. For instance, 1953125. Because I am confused in dividing it into groups!!

    ReplyDelete
    Replies
    1. Okay! As per the rules, divide the number 1953125 into two parts starting three digits from the right and so we get,
      1953 | 125

      On the R.H.S, we have got 1953 and from rule one we see that this number is greater than 10 ( 1000) and so we need to find a number nearer and above 10 that gives the answer closer to it. The cube of 11 is 1331, 12 is 1728 and we see that 1953 is closer to 1728. Hence the answer for R.H.S will be 12.

      On the L.H.S, we have got 125. And according to rule two above, 125 ends in 5 and the answer from the respective table is 5. So, L.H.S, is 5

      Now, R.H.S | L.H.S = 12 | 5

      Therefore, cube root of 1953125 = 125

      Hope you got how it works now :)

      Delete
  9. What would be the cube root of 422875? I have problem about that question and still not finding the answer.I hope,you will help me.

    ReplyDelete
    Replies
    1. Your name instead of anonymous would be better. And that is a tricky question you have asked similar to can you help me find the square root of 27 (or) find a square root of number 10 which we actually know cannot be a whole number like we get for sq.root of 25 = 5 (or) like sq. root of 9 = 3.

      Please note that " The trick of finding cube roots in this post is for numbers that actually work and that which is big to solve without the help of the calculator."

      And for your question, the number you had given is not an actual cube of any number and hence the answer will probably have decimal values which in this case will be 75.###
      Hope I answered to you question :)

      Delete
  10. Anonymous28 July, 2015

    Thnx so much!!!! Really helped in exams

    ReplyDelete
  11. this is really awesome and simple method to find cube ....................:) :) thnks uma

    ReplyDelete
  12. can u please explain this method for the number 4121

    ReplyDelete
    Replies
    1. Hi Hemanth,
      If you have read the post fully, you should have come across that I have written that this technique works only for perfect cubes. The number 4121 is not a perfect cube and hence won't work using this method.

      Delete
  13. Hey uma...can you explain how to get cube root for any 8 or 9 digits perfect cubes??

    ReplyDelete

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