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 $=93$

2015-03-04 02:56:29
How  can we find the cube root of 7 digit number ?
chandan
2015-02-28 10:58:19
how can cube of any no. like 8664, 11565, 465 etc.. other than perfect cube root digit?
simran
2015-02-07 10:37:06
how to find cube root? like, 11 =1331
amit
2015-09-09 03:13:43
1,331

first group having last digit is 1.
hence last digit is 1.

now next group is 1.
subtract 1-1 because cube of 1 is 1. because result should be equal to 0 or > 0.
So ur left digit is 1.

Nikhita
2014-12-03 11:19:27
how to find perfact cube from given 8 distinct number & perfact square
pritam das
2014-10-08 06:50:05
By what smallest number 6300 is to be multiplied to make it a perfect cube ?? sir please ans this prob
Raj
2014-10-14 23:48:57
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
Rajan Pokhrel
2014-09-26 11:04:09
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
Shivakumar E
2015-01-24 11:05:49
Yes I too have same doubt as harish chandra ,If we devise it by three three digits than it vl result 188 as cube root of 2628072.....please clear it
Hari Chandana
2015-01-18 13:25:00
Mr. Rajan Pokhrel, I am just a visitor of this page. I liked this technique. But I have a small doubt!
As you solved the seven digit number 1953125 & 2628072, you divided the groups as:
1953,125 and 2628,072.
But according to the information given in the above examples of this page, it is known that "the groups must be divided in the pattern of three three digits from the right side" But you divided it as "nnnn,nnn" ( I mean four digits, three digits). Is that the correct way to solve this problem?
A page viewer of this helpful site,
Hari Chandana.

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