The roots of a number are a very important topic in Mathematics. They form the basis of a large proportion of trigonometric and arithmetic calculations at higherlevel mathematics. The root of a number is simply another number which if multiplied a certain time to itself will give the same number in return. For ex 2 are the square root of 4 and 2 is also the cube root of 8. That is because if we multiply 2 by itself once we get 4 so we say the square of 2 is 4 and if we multiply 2 by 2 and 2 again then we get 8, which is said as 8 is the cube of 2. This can also be thought from the perspective of dimensions where every time a number is multiplied by itself, a new dimension is added. This same theory is used in the calculation and nomenclature of vector quantities in physics like velocity and acceleration.
How to find the cube root of 9261?
There are two methods to find the cube root of a number. They are:

The Estimation Method.

The Prime Factorization Method.
In this article, we will show the methods to find the cube root of 9261.
To calculate the cube root of 9261 by estimation method, it is important for us to learn the cubes of natural numbers from 1 to 9. These values are easy to learn and help the students to find the cube roots of any number and must be remembered by heart.
How to Determine Cube Root of 9261 by Estimation Method?
In the estimation method, we segregate the number into groups and then estimate its cube root. The steps to be followed while determining the cube root by estimation method is described below.
Step 1:
The given number is divided into groups of 3 digits starting from the rightmost digit of the number. If any number is left out without forming a group of three, zeros are appended to its left to make it a group of 3 digits. However, we must take care that the place value of the digit is not altered by appending zeros.
So, to find the cube root of 9261, we should divide the number into groups of three digits starting from the digit in the unit’s place.
009 261
Step 2:
From the first group starting from the right, note down the unit’s digit.
The first rightmost group in step 1 is 261, and the digit in its unit’s place is 1.
Step 3:
Estimate the digit in the unit’s place of the cube root of the given number using the lookup table given below.
Digit in the Unit’s Place of the Number 
Digit in the Unit’s Place of Its Cube Root 
1 
1 
8 
2 
7 
3 
4 
4 
5 
5 
6 
6 
3 
7 
2 
8 
9 
9 
0 
0 
The digit in the unit’s place obtained in step 1 is ‘1’ and hence the unit’s digit of the cube root of 9261 is also ‘1’.
Step 4:
Now, consider the second group from the right. Check the perfect cube numbers between which this number lies. Suppose the number in this group lies between A3 and B3 and is closer to B3, then the ten’s digit of its cube root is considered as B.
In the given number 9261, the second group of 3 digits from the right is 009.
This number lies between two perfect cube numbers 8 and 27 i.e. 23 and 33. Because 9 is more close to 8 i.e. 23, the ten’s digit of the cube root of 9261 is 2.
The cube root of 9261 found using the estimation method is 21.
9261−−−−√392613
= 21
Prime Factorization Method to Find the Cube Root of 9261
In this method, the number whose cube root is to be found is resolved completely into its prime factors. The identical prime factors are grouped such that three identical factors form one group. To determine the cube root, one factor from each group is collected and multiplied together.
Step 1:
The given number is resolved into its prime factors. It is recommended to start the division with the lowest possible prime number and then go to the higher prime number when the quotient is not completely divisible by the number chosen.
The given number whose cube root is to be determined is 9261. The lowest prime number is ‘2’ and 9261 is not divisible by 2. So, let us go with the next lowest prime number i.e. 3.
9261 when divided by 3 gives 3087 as the answer.
3087 is further divisible by 3. 3087 when divided by 3 gives 1029.
1029 is still divisible by 3. 1029 divided by 3 gives 343.
The number 343 is not divisible by 3 and hence with go with the next lowest prime number. The next lowest prime number is 5. But 343 is not divisible by 5. The next prime number in the queue is 7 and 343 is divisible by 7.
343 divided by 7 gives 49 and 49 divided by 7 is 7. This complete sequence of steps can be summarized as:
Step 2:
Write the number whose cube root is to be determined as the product of their primes.
The number 9261 can be written as the product of its primes as:
9261 = 3 x 3 x 3 x 7 x 7 x 7
Step 3:
Divide the factors into groups consisting of three identical factors.
9261 as the product of its primes is rewritten as:
9261 = 3 x 3 x 3 x 7 x 7 x 7
Step 4:
The cube root of the number is found as the product of one factor taken from each group in step 3.
So, the cube root of 9261 is found to be 3 x 7 = 21
9261−−−−√392613
= 21