What is the digit at units place of the cube root of 2197?

Digit at Unit Place of Cube Root of 2197 is 3

In this article, To determine the digit at the unit’s place of the cube root of 2197, we will use the Estimation method, which involves finding patterns in cubes of single-digit numbers.

But before that let’s know what is cube root of any number is.

Cube of a number obtained by multiplying it by three is the final result. Conversely, the cube root of a number, represented by ∛, is the cube of a number processed backwards. In mathematics, the number (y) that answers the following equation is the cube root of a given number (x).

y³ = x

It may alternatively be written as,

x = ∛y

Cube root is represented by the symbol ∛.

Cube root of any number can be easily found by using various methods that include,

Estimation Method: We must become familiar with the cubes of natural numbers ranging from 1 to 10 to use the estimation method to find the cube root of any number for eg. number = 2197

Let’s now perform a step-by-step calculation of the cube root of 2197 using the estimation method.

Examine the number 2197 that is provided at the unit’s location.

Unit place 2197 has 7.

Take a look at the cubes table above. Examine the cube in the cube table whose number has the digit 7 at the unit’s location.

Clearly, we can see 3³ = 27.

This suggests that the cube root of 2197 has 3 as its unit digit.

We will now ignore the final three digits of 2197, or 197, in order to compute the tenth place of the cube root of 2197.

Using 2 as a reference number, we can observe that the number 2 lies between 1³ and 2³, i.e., between 1 and 8.

Here, we’ll look at the lowest number closest to 2 which is 1.

Since 1³ = 1. Therefore, the tenth place of the cube root of 2197 is 1.

Thus, 13 is the cube root of 2197.

Other Method

Using Cube Root table

• Now, notice the unit’s place of the number 2197, that unit’s place value is 7, look into the above table, and figure out the number that provides a cube value with 7 as unit place digit.
• The number is 3, as the cube of 3 is 27 and the unit’s place value of 27 is 7.

Hence, it can be concluded that the unit’s place value of the cube root of 2197 is 3.

Please note that there are other methods also to find out the cube root of a number like the Prime Factorization method , but it was not directly needed for determining the unit digit using the estimation method.

Conclusion

Digit at the unit’s place of the cube root of 2197 is 3. This is determined using the estimation method by recognizing that 3 is the only single-digit number whose cube (27) ends in 7. Therefore, the unit place digit of ∛2197 is 3