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(80)


pritam das 08 Oct 2014 9:20 AM
By what smallest number 6300 is to be multiplied to make it a perfect cube ?? sir please ans this prob 
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Raj 15 Oct 2014 2:18 AM
prime Factorization of 6300
--------------------------------
6300 = 22 * 32 * 52  * 7
so to make it a perfect cube, 6300 needs to be multiplied with (2*3*5 * 72) = 1470

Required number is = 1470
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Rajan Pokhrel 26 Sep 2014 1:34 PM
I got the solution for seven digit cubes problem, like

find the cube root of 1953125 & 2628072
for 1953125
Solution:
first form it as given rule like
1953,   125
As we know if the last digit of the perfect cube=5, the last digit of the cube root =5
and as we have another rule like
1953-x3 >0
or. 1953- (12)3  >0 (it's true)
and if 1953-133 >0 (it's false)
So, the prefect cube root  of 1953125 = 125

Similarly for 2628072

like,2628,072

As we know if the last digit of the perfect cube = 2, the last digit of the cube root = 8
So for 072 has 8
and for 2628 we have

2628-133 >0 (it's true)

2628-143 >0 (it's false)

So, the prefect cube root  of 2628072 = 138
This way we can solve the problem of  7 digits cube problem
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naveen tewari 08 Sep 2014 12:48 PM

its good technique but explain this? how we calculate cube root of 3048625?

 

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Thiyagarajan 22 Aug 2014 9:12 AM
Great techniques... Super..
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krish 18 Aug 2014 8:57 AM
But sir how to find the cube root of 3048625?
While following the method 3  048  625
unit digit (of cube root) will be 5
cube smaller than  048 is 27 ie 3^3
so ten's digit will be 3 
Hundred's digit will be 1
so by rule we get the cube root is 135
but 135^3 = 2460375
Please clear my confusion 
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amit 02 Aug 2014 1:51 PM

sir its only 6 digits methods means calculated maximum 6 digit and send me 50243409 solved equtions

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hyan 08 Aug 2014 12:12 PM
50243409
ANS- 50  243  409
calculate the nearest cube root of 50=3(smaller than 50) 
then calculate the cube root of 243=6( smaller than 243)
then calculate the cube of 9(UNIT PLACE OF THE NUMBER)=729
SO THE ANS IS-369
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srikrishna 26 Jul 2014 8:05 PM
superb trick

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praveen 19 Jul 2014 12:26 AM
its very useful.
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