Cube Root of 2197

What is Cube Root?

The cube root of a number is the number that, when multiplied by itself three times, equals the original number. For example, the cube root of 8 is 2, because 2 multiplied by itself three times equals 8.

How to Find the Cube Root of 2197

To find the cube root of 2197, divide 2197 by the cube root of 3.

2197 / 3 = 732.33

Cube Root of 2197 by Estimation Method

Now let us proceed to calculate the value of ³√2197 following these steps:

Step 1:

Take the digit present at the unit’s place of 2197.

Unit Place of 2197 has —> 7

Step 2:

Check with the cubes table provided above. The cube of which number has 7 at its unit place?

Clearly, 3³ = 27

That means the cubic root of 2197 will have 3 at the unit place.

Say, ³√2197 = ?3

Step 3:

So, we have got the unit place digit of the required value.

Now ignore the last 3 digits of 2197, i.e. 197

Taking 2 as a reference number, we can see 2 lies between 1³ and 2³, i.e., between 1 and 8.

So, we will choose here the lowest number, nearest to 2, which is 1.

Since, 1³ = 1, therefore, we will have 1 as the first digit of the required number.

Hence, ³√2197 = 13

Cube Root of 2197 by Prime Factorisation Method

Here, we will use the prime factorisation method to find the prime factors of 2197. After that, we will pair the 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 2197

If we try to divide 2197 by any prime number, we will come to know that the smallest prime number which can divide 2197 is 13. Therefore we get;

2197 = 13×13×13

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

2197 = (13)¹⁺¹⁺¹ = (13)³ [By exponent law: a^mxaⁿ = a^m+n]

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

³√2197 = ³√(13)³

The cube root gets cancelled by the cube of 13.

Hence, ³√2197 =13