Question

How to find a cube root ?

Answer 1

Let me explain this with the help of an example.

Say, we need to find the 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.
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 $2^3$ = 8 from 4, 4 - 8 = -4 which is < 0)
Hence the left neighbor digit of the answer = 1.
That is , the answer = 17

Another example- 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 $9^3$= 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

Another basic method is by prime factorization of the number.
Say 4913,
$4913=17\times 17\times 17$
So, cube root of 4913 is 17.