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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)

profileMuskaan Sharan
2020-01-20 15:13:47 
Make a $1$ pair of $3$ from backside
$1061~208$
Now $8^3=512$ we take only $2$ from here
And $10^3=1000$
$11^3=1331$
So we take nearest no that is $10$
Hence,
The ans is $102$
like 0 dislike 0
profileVilas thakur
2014-01-03 08:09:44 
Gm. This is very nice method to find out the cube root of perfect cube . Thanks for info .
like 0 dislike 0 reply
profileEkta
2013-12-10 08:47:27 
how can we find out the cube root of 1906624
like 0 dislike 0 reply
profileSteve
2014-03-02 21:04:06 
make groups 1906 and 624 
end digit of 624 is 4 so last digit is 4
closest cube to 1906 is 1728 which is 12 cube....
therefore the req number is 124
like 0 dislike 0
profileEkta
2013-12-10 08:41:07 
It is very good concept for finding the cube root
like 0 dislike 0 reply
profilesiri
2013-11-12 11:07:42 

hi..

for 123456 i want to find cube root?

456 --last digit 6...

123 near cube is 4 that is 64

so...first elemnt is 4

46

but 46 cube is not 123456

like 0 dislike 0 reply
profileRajan
2013-11-13 18:51:59 
123456 is not a perfect cube
like 0 dislike 0
profilepatrick
2013-11-07 10:42:47 
How about the cube root of the answer of the three digit numbers?
like 0 dislike 0 reply
profilejiss palelil
2014-04-15 07:20:09 
At the beginning, it is already mentioned that we should learn cubes upto 10 which includes all the 3 digits-eg 7 cube, 8 cube etc.....
like 0 dislike 0
profilepatrick
2013-11-07 10:41:20 
how about the three digit number?
like 0 dislike 0 reply
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