Cube roots of perfect cubes Using Vedic Mathematics

It may take two-three minutes to find out cube root of a perfect cube by using conventional method. However we can find out cube roots of perfect cubes very fast, say in one-two seconds using Vedic Mathematics.

We need to remember some interesting properties of numbers to do these quick mental calculations which are given below.

Points to remember  for speedy  calculation of cube roots of perfect cubes

1. To calculate cube root of any perfect cube quickly, we need to remember the cubes of 1 to 10 which is given below.

= 1
= 8
= 27
= 64
= 125
= 216
7³  = 343
= 512
9³   = 729
10³    = 1000

2. From the above cubes of 1 to 10, we need to remember an interesting property.

= 1 => If the last digit of the perfect cube = 1, the last digit of the cube root = 1
= 8=> If the last digit of the perfect cube = 8, the last digit of the cube root = 2
= 27=>If the last digit of the perfect cube = 7, the last digit of the cube root = 3
= 64=>If the last digit of the perfect cube = 4, the last digit of the cube root = 4
= 125=> If the last digit of the perfect cube =5, the last digit of the cube root = 5
= 216=> If the last digit of the perfect cube = 6, the last digit of the cube root = 6
7³  = 343=> If the last digit of the perfect cube = 3, the last digit of the cube root = 7
= 512=> If the last digit of the perfect cube = 2, the last digit of the cube root = 8
9³   = 729=>If the last digit of the perfect cube = 9, the last digit of the cube root = 9
10³    = 1000=>If the last digit of the perfect cube = 0, the last digit of the cube root = 0

 

It’s very easy to remember the relations given above because

-> (Same numbers)
8 -> 2 (10’s complement of 8 is 2 and 8+2 = 10)
7 -> 3 (10’s complement of 7 is 3 and 7+3 = 10)
4 -> 4 (Same numbers)
5 -> 5 (Same numbers)
6 -> 6 (Same numbers)
3 -> 7 (10’s complement of 2 is 7 and 3+7 = 10)
2 -> 8 (10’s complement of 2 is 8 and 2+8 = 10)
9 -> 9 (Same numbers)
0 -> 0 (Same numbers)

 

Also See
8 ->  2 and 2 ->  8
7 -> 3 and 3-> 7

If we observe the properties of numbers, Mathematics will be a very interesting subject and easy to learn.Now let’s see how we can actually find out the cube roots of perfect cubes very fast.

Example 1:  Find Cube Root of 4913

Step 1:

Identify the last three digits and make groups of three three digits from right side. That is 4913 can be written as            
4,   913

Step 2

Take the last group which is 913.  The last digit of 913 is 3.

Remember point 2, If the last digit of the perfect cube = 3, the last digit of the cube root = 7

Hence the right most digit of the cube root  = 7

Step 3

Take the next group which is 4 .

Find out which maximum cube we can subtract from 4 such that the result >= 0.
We can subtract 1³ = 1 from 4 because 4 - 1 = 3 (If we subtract 2³ = 8 from 4,   4 – 8 = -4 which is < 0)

Hence the left neighbor digit of the answer  = 1.

That is , the answer = 17

 

Example 2:  Find Cube Root of 804357

Step 1:

Identify the last three digits and make groups of three three digits from right side. That is 804357 can be written as            
804,   357

Step 2

Take the last group which is 357.  The last digit of 357 is 7.

Remember point 2, If the last digit of the perfect cube = 7, the last digit of the cube root = 3

Hence the right most digit of the cube root  = 3

Step 3

Take the next group which is 804 . Find out which maximum cube we can subtract from 4 such that the result >= 0. We can subtract 9³ = 729   from 804 because 804 - 729    = 75 (If we subtract 10³ = 1000 from 729   ,   729    – 1000 = -271 which is < 0)

Hence the left neighbor digit of the answer  = 9

That is , the answer = 93


Comments(64)
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showing 1-10 of 64 comments,   sorted newest to the oldest

Manoj (Alex)
2015-07-29 09:19:57 
How to find cube root more than 6 digit
(0) (0) Reply
Anduna Abdul
2015-07-21 18:43:08 
this method is only applicable for finding cube root upto 6 digit numbers.  But very nice though.
(0) (0) Reply
chithiraivel
2015-07-15 05:05:47 
how to find a cube root of a simple number other than perfect cube?
(0) (0) Reply
Raywant Bhatia
2015-06-17 08:12:35 
How to find cube root of 10 digit no.
(0) (0) Reply
swarup
2015-07-10 18:57:24 
for that u need to know the cube of 10-20 or may be 20-30.
process is all same u have to solve unit digit rule as above then neglect last 3 digits and find the no whose cube value is nearest to remaining 7 digits.

if u cant then do again or reply back.
(0) (0) Reply
Md.Arman
2015-05-30 01:52:16 
I have read all the process, it was very interesting but I may like to know how to find the cube root of a decimal and what if the cube root of the number is in decimal?
(0) (0) Reply
nivedita
2015-04-21 09:54:56 
how to find cube root of a number which is in decimal?
(0) (0) Reply
Darshan Moradiya
2015-03-04 02:56:29 
How  can we find the cube root of 7 digit number ?
(0) (0) Reply
chandan
2015-02-28 10:58:19 
how can cube of any no. like 8664, 11565, 465 etc.. other than perfect cube root digit?
(0) (0) Reply
simran
2015-02-07 10:37:06 
how to find cube root? like, 11 =1331
(0) (0) Reply
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