 # Cube Root of 9261

The cube root of 9261, denoted as 3√9261, is equal to a value which gives the original number, i.e., 9261 on multiplied by itself, three times. Basically, cube root of number is the root of a cubed number. In other words, if a3 = b, then 3√b = a. Therefore, the cube root is the reverse method of evaluating a cube.

 Cube root of 9261, 3√9261 = 21

Let 3√9261 = x, then 9261 = x3. So, we need to find here the value of x. Now, if we do the prime factorisation method of 9261 it will take more time. Hence, the fastest method to find the value of 3√9261 will be by the estimation method, which is recommended for all the numbers having more than or equal to 4-digits.

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## Cube Root of 9261 By the Estimation Method

To learn this method we need to memorise the value of cubes from 1 to 10. These values are easy to keep in mind for each student and will also help to do a quick calculation. Here is the table of cubes 1 to 10, for reference.

 Number Cubes (n3) 1 1 2 8 3 27 4 64 5 125 6 216 7 343 8 512 9 729 10 1000

Now let us proceed to calculate the value of 3√9261 following these steps:

Step 1:

Take the digit at the unit’s place.

Unit Place of 9621 has —> 1

Step 2:

Check with the cubes table provided above. The cube of which number has 1 at its unit place.

Clearly, 13 = 1

That means the cubic root of 9261 will have 1 at the unit place.

Step 3:

So, we have got the unit place digit of our answer.

Now ignore the last 3 digits of 9261, i.e. 261

Taking 9 as a reference number, we can see 9 lies between cube of 2 and cube of 3, i.e., between 8 and 27.

So, we will choose here the lowest number, nearest to 9, which is 8.

Since, 23 = 8, therefore, we will have 2 as the first digit of the required number.

Hence, 3√9261 = 21

## Cube Root of 9261 by the Prime Factorisation Method

Here, we will use the prime factorisation method to find the prime factors of 9261. After that, we will pair identical prime factors in a group of three to represent them as cubes. Since the cubes of a number cancel the cube root, therefore we will get the required value.

Let us understand step by step:

Step 1: Find the prime factors of 9261

9261 = 3×3×3×7×7×7

Step 2: Pair the identical factors in a group of three and write in the form of cubes.

9261 = (3×3×3)×(7×7×7)

9261 = 33×73 [By exponent law: amxan = am+n]

9261 = (3×7)3 [By exponent law: amxbm = (ab)m]

9261 = 213

Step 3: Apply cube root to both sides of the above expression.

3√9261 = 3√(213)

The cube root gets cancelled by the cube of 21.

Hence, 3√9261 =21