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 end 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 -
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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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March 29th, 2013 - 21:36
dis process is really correcct and very very help full !!! … its amazing !!
November 19th, 2012 - 13:16
Thanks quicker maths.com,,, it is really very helpful in order to find the cube of any number !!!Keep it up good job
September 12th, 2012 - 00:42
vineet Bhaiya I got info abt this site from google wen i was practising acct in the mid ni8 suddenly i got a sum where relation of cost and sales was required.I saw the trick you learn from jha sir and i completed the sum. Thank you very Much Bhaiya
Your site and your help to students like me is awsome.
March 29th, 2013 - 23:31
Ayush, thanks for sharing your experience. I’m glad that the trick helped in you.
September 11th, 2012 - 15:35
actually cube root of any no can be found very easily.(even not perfect cubes). let 123456 is a no. now from the units place mark every tthree digits. for eg. here mark 456 nd 123. now find the nearest cube to 123. it is(4 cube) ie 64. nw subtract 64 from 123. now gthe remainder is 59. nw bring down the remaining no. therefore the no formed is 59456.
then, in the eqtn, 300x^2y + 30xy^2 +y^3=59456(nw put the value of x=4) therefore the eqtn will be 4800y + 120y^2 + y^3. nw by trial and error method put the values of y in the eqtn nd find for which value of y the no formed will be the nearest to 59456. therefore (40+y) is the nearest cube root of 123456. this can be done for any no.
September 11th, 2012 - 15:35
i am a student of class 9. if i am wrong friends then tell me. it is a time of learning. to mr. vineet am i right?///////////////
September 3rd, 2012 - 16:45
how to know a number is a perfect square or cube in vedic math way?
September 11th, 2012 - 15:37
see my way plz/
September 3rd, 2012 - 16:26
it wud benefit a lot. thanx
August 26th, 2012 - 20:03
It is very nice Trick to find the Cube Root of maximum 6 digits quickly ! Thanks for giving us Tricks .
August 22nd, 2012 - 00:45
It is nice to see cube root of maximum 6 digit numbers we will discuss here when the number is more than 6 digits and it is perfect cube too .
Find cube root of 34965783
Group the 3 digit groups stating from right to left i.e. 34/965/783 it shows that the cube roots will have 3 digits as there are 3 groups .So n=3
The first digit of cube root will be decided by the first group i.e 34 as 34 lies between 27& 64 and cube roots are between 3 and 4 The smaller of these two will be taken that is 3
F=3
The last digit of cube root is decided by 783 which is ending in 3 means cube ending in 3 gives cube root ending in 7 so last digit i.e L=7
F=3; L=7 ;and n=3x
Step 1 :-L*L*L=7*7*7=343 subtract 343 from 34/965/783 we get 34/965/44
Step 2 :-For next digit of cube root we calculate 3 *L*L*K =3*7*7*K=147K The last unit digit at extreme right is 4 which can be achieved only when K=2 (because 7 of 147 multiplied by 2 gives 4 in units place)
Step 3 :- The answer is F K L i.e 327 is cube root of 34965783
Find Cube root of 77145562593
Step 1 :- Group of 3 starting from right to left i.e 77/145/562/593 there are 4 groups so n=4
Step 2 :- First digit will be from first group i.e 77 whose roots lies between 4 and 5 we will take smaller therefore F=4
Step 3 :- Last digit will be given by last group i.e 593 the cube ending in 3 so the cube root ends in 7 therefore L=7
Step 4 :- L*L*L=7*7*7=343 subtract 343 from 77/145/562/593 we get 77/145/562/25
Step 5 :- 3*L*L*K= 3*7*7*K=147K (last digit is 5 ) Therefore K=5 ( 7 multiply by 5 only gives 5 in units place) and 147*5=735 subtract 735 from 77/145/562/25 we get 77/145/554/9
Step 6 :- 3*L*L*J+3*L*K*K=3*7*7*J+3*7*5*5=147*J+525 ( Last digit is 9) which means J=2 will fetch 9 In the units place
Step 7 :- Answer is F J K L i.e 4257 is the required cube root
August 21st, 2012 - 23:16
It is nice to see cube root of maximum 6 digit numbere we will discuss here when the number is more than 6digits and it is perfect cube too .
Find cube root of 34965783
Combining the 3 digit groups stating from right to left i.e. 34/965/783 it shows that the cube roots will have 3 digits as there are 3 groups.So n=3
As first digit of cube root will be given by First group from left i.e. 34 we know that 34 lies between 27 and 64 which are cubes of 3 and 4 so the first w3 digits the remaining digit is middle digit
F=3 ; L=7 ;and n=3
(L) L=7 therefore L cube =7*7*7=343
substracting 343 from 34/965/783 we get 34/965/44
(K) 3L*L*K=3*7*7*K=147K ( ending in 4) therefore K=2 ( because 7*2 only gives 4 at units place)
The answer is F K L i.e 327
July 24th, 2012 - 14:29
what to do with these ugly ad. which is hiding the trick do some thing
July 4th, 2012 - 20:53
very interesting and nice technique … pls send and share if u know more such techs ……………………thank you
June 12th, 2012 - 11:25
the above method is very useful but what if the number is not a perfect cube
e.g. 1351. if the above method is applied in this number we find that it is cube of 11 but it’s not true as 11′s cube is 1331.
kindly help to find the cube or cube root of any number whether it is perfect cube or not
June 28th, 2012 - 00:15
MR.RAHUL,
IF YOU KNOW THE METHOD TO FIND THE CUBE ROOT OF NOT PERFECT CUBE, PLEASE TELL ME, I NEED THE ANSWER.
September 11th, 2012 - 15:30
actually cube root of any no can be found very easily.(even not perfect cubes). let 123456 is a no. now from the units place mark every tthree digits. for eg. here mark 456 nd 123. now find the nearest cube to 123. it is(4 cube) ie 64. nw subtract 64 from 123. now gthe remainder is 59. nw bring down the remaining no. therefore the no formed is 59456.
then, in the eqtn, 300x^2y + 30xy^2 +y^3=59456(nw put the value of x=4) therefore the eqtn will be 4800y + 120y^2 + y^3. nw by trial and error method put the values of y in the eqtn nd find for which value of y the no formed will be the nearest to 59456. therefore (40+y) is the nearest cube root of 123456. this can be done for any no.
July 3rd, 2012 - 22:23
Hi v cant able to find for non-perfect numbers ths tech s nly for cube…..
August 22nd, 2012 - 12:42
We should always cross check the results of these mathematical tricks. The best way to check these results is Digit sum method which suggests that the sum of digits at left should be equal to the sum of digits at right side if our results are correct.
If 11^3= 1351
11*11*11= 1351 (sum of 11 is 1+1=2)
2* 2* 2 =1+3+5+1=10
8 = 1+0=1 which is not correct so the answer 11^3=1351 is wrong
May 29th, 2012 - 13:15
Gud One ..very simple compared to division method
May 25th, 2012 - 20:58
thnx….
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
November 30th, 2012 - 13:31
I would like to thanks for the time you have cunoribtted in writing this article. I am hoping the same best blog post from you in the upcoming as well. In fact your creative writing skill has inspired me to get my own blog now. Truly the blogging is spreading its wings rapidly. Your write up is a fine model of it.
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.
November 30th, 2012 - 13:56
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June 28th, 2012 - 00:21
GREEN , CAN YOU TELL THE METHOD CLEARLY, AND FOR NOT A PERFECT CUBE, PLZ SEND THE EXPLANATION
September 27th, 2012 - 20:51
its really amaizing
thnx sir
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