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(72)


srikrishna 26 Jul 2014 10:35 AM
superb trick

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praveen 18 Jul 2014 2:56 PM
its very useful.
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kava ram 10 Jul 2014 11:55 AM
Wt abt non perfect numbers
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EROL CURMAK 09 Jul 2014 1:30 PM
Wonder how is it with no exact cube roots. Jagadguru Swami Sri Bharati Krishna Tirthaji Maharaja had that extracting too in his book vedic Mathematics, but I have problems, need help
Thanks
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rishika 26 Jun 2014 4:46 AM
i like maths but after this i love maths
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chirag agartwal 22 Jun 2014 8:33 AM
yes it very nice
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shriram 05 May 2014 1:24 PM
awesomme
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priya 27 Apr 2014 3:50 PM
how can we find the cube root for non perfect cube

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Pritam Kumar Kar 26 Apr 2014 2:35 AM
How to find cube root for numbers greater that 6 digit like for 1061208
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philip 21 Apr 2014 2:41 AM
awesome
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