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Cube Roots of Perfect Cubes Using Vedic Mathematics

Cube roots of perfect cubes can be found out faster using Vedic Mathematics.

Points to remember

1. To calculate cube root of any perfect cube quickly, we need to remember the cubes of $1$ to $10$ (provided below).

$1^3=1\\2^3=8\\3^3=27\\4^3=64\\5^3=125\\6^3=216\\7^3=343\\8^3=512\\9^3=729\\10^3=1000$

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

$1^3=1$ $\Rightarrow$ If last digit of perfect cube $=1,$ last digit of cube root $=1$
$2^3=8$$\Rightarrow$ If last digit of perfect cube $=8,$ last digit of cube root $=2$
$3^3=27$$\Rightarrow$ If last digit of perfect cube$=7,$ last digit of cube root $=3$
$4^3=64$$\Rightarrow$ If last digit of perfect cube$=4,$ last digit of cube root $=4$
$5^3=125$$\Rightarrow$ If last digit of perfect cube $=5,$ last digit of cube root $=5$
$6^3=216$$\Rightarrow$ If last digit of perfect cube$=6,$ last digit of cube root $=6$
$7^3=343$$\Rightarrow$ If last digit of perfect cube$=3,$ last digit of cube root $=7$
$8^3=512$$\Rightarrow$ If last digit of perfect cube$=2,$ last digit of cube root $=8$
$9^3=729$$\Rightarrow$ If last digit of perfect cube$=9,$ last digit of cube root $=9$
$10^3=1000$$\Rightarrow$ If last digit of perfect cube$=0,$ last digit of cube root $=0$

It’s very easy to remember the relations given above as follows.

$1\implies 1$same numbers
$8 \implies 2$$10$'s complement of $8$ is $2$ and $8+2=10$
$7 \implies 3$$10$'s complement of $7$ is $3$ and $7+3=10$
$4 \implies 4$same numbers
$5 \implies 5$same numbers
$6 \implies 6$same numbers
$3 \implies 7$$10$'s complement of $3$ is $7$ and $3+7=10$
$2 \implies 8$$10$'s complement of $2$ is $8$ and $2+8=10$
$9 \implies 9$same numbers
$0 \implies 0$same numbers

Also see
$8 \implies 2$ and $2 \implies 8$
$7 \implies 3$ and $3 \implies 7$

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

Example 1: Find Cube Root of 4913

Step 1

Identify the last three digits and make groups of three three digits from right side. i.e., $4913$ can be written as

$4,\quad 913$

Step 2

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

Remember point 2, If last digit of perfect cube$=3,$ last digit of 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 $\ge 0$

We can subtract $1^3=1$ from $4$ because $4-1=3$ (If we subtract $2^3=8$ from $4,$ $4-8=-4$ which is $\lt 0$)

Hence the left neighbor digit of the answer $=1$

i.e., 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. i.e., $804357$ can be written as

$804,\quad 357$

Step 2

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

Remember point 2, If last digit of perfect cube $=7$ , last digit of 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 $\ge 0$

We can subtract $9^3=729$ from $804$ because $804-729=75$ (If we subtract $10^3=1000$ from $729,$ $729-1000=-271$ which is $\lt 0$)

Hence the left neighbor digit of the answer $=9$

i.e., answer $=93$

Comments(69)

profileandy
2013-11-03 23:05:51 
But he asked a good quest.plz try to apply the aforesaid formula to calculate cube root of 41063625. I was not able to do it..
like 0 dislike 0 reply
profileKumar Pradeep
2013-10-02 15:00:02 
Dear Mam,

As per the aforesaid procedure, when i came to extract the Cube root of 5637, the Ans. is 13  but it is nt a correct ans.
And 2ndly it is mentioned that we can get the cube root of a PERFECT CUBE DISIT. anyway, How Can I know that, a no. whether is a PERFECT CUBE OR IMPERFECT CUBE ???

Plz clarify.

Thanking you,
With Regards.
like 0 dislike 0 reply
profileBionic Man
2013-10-18 13:00:17 
Its not a perfect cube,i have asked to God(google) regarding the same and he replied with 17.7919 which is not a perfect cube,this method applies only for perfect cube

Thanks
ccb
like 0 dislike 0
profilerahul
2013-09-18 10:54:13 

 when we subtract the cube to get the last digit, it should be >=0 its ok.

 

But if its 1 or -1 , than also it should be correct .

 

 

Pls note. Which was not written

like 0 dislike 0 reply
profileashwini
2013-09-13 10:52:14 
why want we take 9
like 0 dislike 0 reply
profiledattatraya
2013-09-18 11:19:17 

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
like 0 dislike 0
profileBhuban
2013-09-16 10:26:10 
9³ = 729  & 10³ = 1000
We can subtract 9³ = 729   from 804 because 804 - 729    = 75 (If we subtract 10³ = 1000 from 729   ,   729    - 1000 = -271
 we have to consider about the different between the two substraction.
like 0 dislike 0
profileMukesh kumar
2013-09-02 11:01:18 
what is the cube root of 41063625   ?
like 1 dislike 0 reply
profilearoo
2013-09-18 11:23:09 
whether do u need for competitive exam no na then  6 digits nos  r given  in the exam not ur no 41063625 
like 0 dislike 0
profileMathsM
2013-08-27 12:43:56 
how to find the cube root of 9 digit number
like 0 dislike 0 reply
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