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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)

profilejayashankar
2013-06-14 05:07:57 
Kindly publish these kinds of shortcuts.
like 1 dislike 1 reply
profilekirti kumari
2013-05-27 09:07:08 
how to find the 3 digit number cube root?
like 0 dislike 0 reply
profilepurbash
2013-05-01 11:20:56 
Is there any test to find weather a number is a perfect cube or not??
like 0 dislike 0 reply
profileV
2013-04-08 14:21:07 
How to find cube root of 7 digit No. ?
like 0 dislike 0 reply
profileveerachari
2013-04-16 07:58:27 
here we take 10 -which digit's cube do you want know(except 4,5,6,9)

for example :you want to find cube root of 7 digit No.
here 10-7=3 is unit digit of cube root of 7 =343
 suppose u want to find out cube root of 3 we using this formula 10-3=7
cube root of 3=27 here unit digit is 7
like 0 dislike 0
profilesolasu
2013-02-10 17:28:00 
This method is limited to only two digits what about more than two digits
like 0 dislike 0 reply
profileHemant
2012-09-08 09:44:25 
Very awsome trick to find the cube root of any number....i really impressed !!!!!!!!!!!
like 0 dislike 0 reply
profileRamkumar
2012-08-29 06:43:30 
maths shortcuts on cube, cube roots, square, square roots, multiplication and many other shortcuts
like 0 dislike 0 reply
profileRiya Mishra
2012-08-16 18:51:38 
want to know how to fintout cuberoot of any number using vedic method
like 0 dislike 0 reply
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