Finding Cube Root – Vedic Maths Way
This is an amazing trick which was always appreciated by the audience I have addressed in various workshops. This awe inspiring technique helps you find out the cube root of a 4 or 5 or 6 digits number mentally.
Before going further on the method to find the cube root, please make a note of the following points –
1) Cube of a 2-digit number will have at max 6 digits (99^3 = 970,299). That implies if you are given with a 6 digit number, its cube root will have 2 digits.
2) This trick works only for perfect cubes, it will not work for any arbitrary 6-digit
3) It works only for integers
Now let us start with the trick to find cube root of a 5 or 6 digit number in vedic mathematic way.
Say you have to find the cube root of 54872. It is known that it’s a perfect cube.
Now divide this number into two parts. The right hand side should always have 3 digits. Remaining digits will come in left hand side. Do it as shown below.
54 | 872
You know the answer will have 2 digits. Digit at tens place and digit at units place. We will get the digit at tens place using the left hand side of the original number (54) and digit at units place using right hand side of the number (872)
Step 1.
Memorize these tables (very soon you will know why) –
Table 1: Cube of 1 to 10
| Number | Cube |
| 1 | 1 |
| 2 | 8 |
| 3 | 27 |
| 4 | 64 |
| 5 | 125 |
| 6 | 216 |
| 7 | 343 |
| 8 | 512 |
| 9 | 729 |
| 10 | 1000 |
Table 2: Unit’s digit of Cube Roots
| Cube Ends in | Cube Root Ends in |
| 1 | 1 |
| 2 | 8 |
| 3 | 7 |
| 4 | 4 |
| 5 | 5 |
| 6 | 6 |
| 7 | 3 |
| 8 | 2 |
| 9 | 9 |
| 0 | 0 |
Step 2.
For left hand side we need to use table 1. We have to see between which 2 numbers in the 2nd column do 54 lies. In this case it lies between 27 and 64. So we will take the cube root of the smaller number i.e. 27 which is 3.
So 3 is the tens digit of the answer.
Step 3.
For right hand side we need to use table 2. Since our original number (the perfect cube) ends in 2 (see 54872), its cube root will ends in 8.
Thus the units digit will be 8.
Combining the results we get the answer as 38.
Thus (54872)^1/3 = 38
Try for perfect cubes like 185193, 42875, 1728.
You might also be interested in the trick of finding square root of any number
I hope you liked the simple trick to find the cube root. Leave your comments below -
You may also like:
- Shortcut to find the Cube of a number
- Speed Multiplication by 111 : Vedic Maths
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Who is behind QuickerMaths?
I am Vineet Patawari - PGDM (IIM Indore), ACA, B.Com(H). My passion for Mathematics, specially Vedic Maths encouraged me to start QuickerMaths
I believe that if trained properly using powerful tools like Vedic Maths, the immense intellect of human mind can be ignited instantly - find out more
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Recent Comments
akbar said that one should get the ring back without climbing into the well. so,birbal... – 18May12
Really thanks .... hats of you ... please tell me such a important tricks of... – 18May12
Very nice – 16May12
Hey, i think the question ll be like : A and B separately can do... – 13May12
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May 18th, 2012 - 00:02
Really thanks ….
hats of you …
please tell me such a important tricks of math and reasoning i am getting very tired of doing such a long problems …
please.. send me on nilesha2010@gmail.com
thank you..
April 18th, 2012 - 16:58
Its a very nice trick to find the cube root……
April 9th, 2012 - 22:53
it’s a matter of understanding…
but the tecnique is wowfull..
April 7th, 2012 - 16:50
Its so simple to find cube root…..
March 26th, 2012 - 11:26
Amazing……………………………….. Thanks for sharing this trick. Its really helpful. God bless Vedic Mathematics
March 23rd, 2012 - 11:44
simply smarter way . just outstanding
March 8th, 2012 - 00:55
hw could v knw dat it is a perfect cube???????????????????????
otherwise dis method will nt b useful 4 any1!!!!!!!
March 2nd, 2012 - 14:03
Thanks for sharing, its very useful for teaching and learning.
February 21st, 2012 - 12:21
I have learnt this method in a sir named Dhawal Bhatia’s class but I had forgetten it. I wanted to remember it again and so you did it
THANK YOU VERY MUCH .
February 21st, 2012 - 00:16
even more simply for XY cubed to make FEDCBA
- “A”the last digit of the answer corresponds to Y cubed only
& FED corresponds to X cubed only (as even if Y=9 it’s cube is only 729 & can’t influence the tens of thousands column)
February 20th, 2012 - 22:29
- Actually I can see it’s even easier than this, you only need to learn the one table not two. Once you learn the first table you know the cube roots of the numbers 0-9
so if XY cubed = FEDCBA
then find X by looking at the range of FED
then find Y by looking at the last digit of A cubed
e.g. 250047 ..so X=6, 7 cubed=343 so Y=3
so the number is 63
of course when you’ve done it a few times you’ll find you’ll automatically have the 2nd table in your head and know Y straight away from looking at “A”
March 26th, 2012 - 11:28
Really its amazing sir. Please share some more methods.
February 17th, 2012 - 15:15
thnx a lot mn!!! cheers..
really helpful
February 15th, 2012 - 00:57
its really wonderful method
January 28th, 2012 - 03:44
la radice cubica si fa con carta epenna e senza simboli solo numeri prova a fare questa è piccola cifra
January 17th, 2012 - 18:10
hiiiiiiiii i wntt to accurate ans ths method use only nearby ans soo plz another shrtcut to solve cube root
January 13th, 2012 - 15:51
it’s really a quicker math it’s best for immediate calculations
January 12th, 2012 - 18:05
nothing surprise as its already in our books named as Taking cube root through estimation. N same is for square root as well. But yeah this is good if it is displayed on this site.
January 12th, 2012 - 18:03
well nothing surprise as we have this method in book named as taking cube root through estimation. Same is for square root as well. But yeah good if it is displayed on this site
December 12th, 2011 - 10:57
amazing in fact in from a small town nobody helps me for this method but now can solve my cube much more speed
December 5th, 2011 - 16:12
superb………….
really helped me with my calculations and also with my exams !!!!!!!!!
November 30th, 2011 - 20:08
No comments………. superbbb…….
November 28th, 2011 - 16:02
It is very easy to find out cube root using the method. Good tactics!!
November 21st, 2011 - 18:46
Really Handsoff . tx admin
November 19th, 2011 - 09:31
Thanks sir….it is a very nice trick
But I have a confusion
how will we find out that if a number is perfect cube or not??
November 13th, 2011 - 10:11
simply superb!!!
November 10th, 2011 - 21:03
this trick is simply superb! it will help a lot in our speedy calculations
November 7th, 2011 - 19:33
It was realy a nice trick to find the cube root