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
- Multiply 2 numbers, sum of whose unit places is 10
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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October 31st, 2011 - 19:23
thanks a lot……..very helpful
:)
October 30th, 2011 - 21:36
how to find cube roots of eqn
X^3+X^2-15X+2=0
October 17th, 2011 - 10:44
How to find out Qube of 1284
October 31st, 2011 - 19:21
first check the digits….its ly 4 and closer to 1000. so it lies btwn 10^3 to 11^3……..so its not a perfect cube……. as we know 10^3 is 1000 and 11^3 is 1331…….
September 26th, 2011 - 13:18
very useful for bank exam…
thanks lot….
give me more………………….
September 16th, 2011 - 10:57
I m still confused….. plz explain in brief…… Can u?
September 8th, 2011 - 12:13
oh my god…thnak u thank u thank u sooooooo much…i m js preparing for mba….n this trick will definetly work out….:-):-):-)
September 26th, 2011 - 13:19
hi soumi…
August 27th, 2011 - 00:04
अनुमान लगाकर संख्या,
करो विभाजित,
छोड़ो आधा पाधा।
भागफल व संख्या का जोड़,
विभाजित कर दो आधा आधा ॥यदि वर्ग पूर्णांक संख्या का है तो यह विधि अधिक उपयोगी है। यह विधि अनुमान पर अधारित है। सही उत्तर के लिए गुरू की अन्य विधि प्रयोग करें
उदाहरण: 5929 का वर्गमूल कितना होगा
अनुमानित उत्तर 70, 5929 को 70 से भाग देने पर भागफ़ल 84,
भागफल व अनुमान का योग 70+84= 154, वर्गमूल 154 का आधा यानी 77
” भूलना भूल जाओगे” पुस्तक से साभार
August 23rd, 2011 - 23:38
what a gr8 ancient science given by india mathematics
August 9th, 2011 - 13:08
kamal ho gaya…
August 2nd, 2011 - 09:23
Amazing tricks, really!!
July 24th, 2011 - 16:38
mStaM h yR..ndd ThanX$ a lohT..xD xD x))
July 23rd, 2011 - 03:11
Hey webmaster! thanks for the info!
July 5th, 2011 - 18:55
superb……!
June 15th, 2011 - 11:58
how we know the number is a perfect cube……….
June 13th, 2011 - 22:02
cool one…..thanx a lott..!
June 12th, 2011 - 00:11
awesome dude……..u love this subject more than your GF. aren`t u?
June 11th, 2011 - 13:03
thanks buddy it really brings difficulties easier for student
May 23rd, 2011 - 22:51
Lovely…………..Its wonderful……………it helped me alot now i am doing engineering
………………….:)
i ma so ecited
April 19th, 2011 - 10:59
very nice tric. this will useful for banking exams
April 17th, 2011 - 12:39
i saw your theory , you told about a perfect cube number , but if i have to find the cube root & square root of that number which is not a perfect cube or not a perfect square, then how will i find ……reply me early
March 12th, 2011 - 00:04
its really helpful to know the result of the square root
June 7th, 2011 - 14:20
hey friend i m also preparing for bank po since 2 months can you help me in maths for shortcut tricks
March 4th, 2011 - 20:47
wow…this rocks………thanks to vedic maths
May 23rd, 2011 - 22:52
i know it acctually rocks………….
February 27th, 2011 - 14:13
super
February 26th, 2011 - 21:48
excellent
February 8th, 2011 - 04:53
Could you please help me to find the square of 32.77?
January 30th, 2011 - 16:19
how to calculate
(2 raise to -3) divided by (2 raise to 3)
Plse explain
March 7th, 2011 - 22:33
very easy ,as 2^3 when goes in numerator it becomes 2^-3 the answer is 2 raise to the power-6
January 16th, 2011 - 15:48
ossum! quickermathematics will make others quick.
January 10th, 2011 - 14:05
this is something i was looking for from long time, thanks for saving my such a valuable time.
February 12th, 2011 - 12:36
beta 458 is nt a cube of any no.
December 25th, 2010 - 17:53
it doesn’t work for (458)^3 and many others above 100
January 12th, 2011 - 19:10
this method is only for 6 digit number or less than that
not for more than 6 digit number
December 13th, 2010 - 17:25
Best methord. Saves time and proves you Smart.
December 6th, 2010 - 17:00
But wat abt non perfect cubes buddy please please send me a text or any doc containing this finding cuberoot of any number please
November 30th, 2010 - 12:17
bole to aikdam jhakhas…………
November 15th, 2010 - 03:38
Could you make a video with a tutorial on how to find the cube root of a 9 digit number??
November 14th, 2010 - 18:27
how do we calculate the cube root of 700 227 072. It has 3 triplets. that is CR will have 3 digits, Hundreds- tens and unit.
Secondly what’s the procedure to calculate the product of 3 digit by 3digit by 3 digit numbers. e.g. 231*342*515 or
42*34*15
I will be glad if i get the algebraic proof for both. thanx. mukund
November 1st, 2010 - 14:28
Just too simple and amazing!
1. I see is that we should know that the given number is a perfect cube!
2. This will only apply to cubes of two digits. I do not believe we can use this method to find Cube Root of 1771561 (Ans. 121).
3. How about 3511.808 (Ans. 15.2)?
Nandesh, your solution is wonderful. But I need Excel to do it.
November 1st, 2010 - 13:58
this trick is really splendiferous
heads of u
October 28th, 2010 - 13:09
Superrrrrrrrrrrrr ra babu
Awsommmmmmmmmmmmmmmmme
October 13th, 2010 - 00:29
man great trick u are amazing keep it up…..nice one
October 6th, 2010 - 16:23
it is amazing one ,so thanks to vedic maths
September 30th, 2010 - 20:23
its quite interesting!! love maths!!!!
August 19th, 2010 - 23:06
awesome.but i suggest u give more examples for better understanding.
still,it was tooooooooooooooooooo helpful to me!!!
thanx
August 19th, 2010 - 03:53
this sooooooooooooooooooooooooooooooooooooooo hard
hate maths but this helps
August 7th, 2010 - 17:00
is there no other easier method to find square root and cube root??
July 30th, 2010 - 03:25
Amazing,really!!
Prior ,I used to scare by seeing long digits ‘s cube root calculations.
It is very precise and to the point for the learner .
It ‘s great..
Thanks.
July 8th, 2010 - 08:27
Great site. A lot of useful information here. I’m sending it to some friends!
June 29th, 2010 - 12:41
plzzzzz mail the result to me @ shona.garveeta@gmail.com……
June 29th, 2010 - 12:40
wow……amazing trick..really..its fantabuluous……
well can i know the shortcut for finding the cube root of a decimal no. like…3.61*10000000………..????
June 3rd, 2010 - 17:08
One general method to find any root is by Heron’s method:
This is applicable for any numbers.
Ex: To find the Cube root of 50000.
Step 1. Make a initial guess of the cube root. (the estimate cane be as good or as bad as you like). Let it be 30.
Step 2: Divide the number by the estimate twice.
50000 / 30 = 1700
1700/30 = 57
Take the average of 30 + 30 + 57 which is 39.
This is the second estimate for the required root.
Repeat the same process above till you get the root with the required accuracy.
Tip: In the initial iterations, divisions need not be be done accurately.
This method is applicable for roots of any degree – square root, cube root, fourth root or fifth root or whatever.
June 3rd, 2010 - 17:32
@Nandeesh – Thanks a lot for your suggestions. I request you to send me a simple description of Heron’s method, so that I can post it in your name on QuickerMaths.com
You can mail this to me @ vineetpatawari@gmail.com
Thanks again
June 15th, 2011 - 12:07
i can’t get this please explain me in brief… thanks and regards.
June 2nd, 2010 - 14:21
@Manish: Thanks
June 2nd, 2010 - 13:27
amazing tric. i have no words for this tric