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

Digit at Unit Place of Cube Root of 2197 is 3

Number system is easily represented on a number line and Integers, whole numbers, natural numbers can be all defined on a number line. The number line contains positive numbers, negative numbers, and zero. Number system is defined in two ways, the Indian and International way of writing numbers, in Indian style, the commas are added from right to left. The numbers are defined with the unit place, tens place, hundreds, and so on.

What is Cube Root?

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 ∛.

Methods to Find Cube Root of a Number

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

Estimation Method: We must become familiar with the cubes of natural numbers ranging from 1 to 10 in order 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.

Prime Factorization Method: Here, we’ll talk about how to find the prime factors of 2197 using the prime factorization method. We will pair the factors in a group of three and write them as cubes once we have identified the prime factors of 2197. We obtain the desired value when the cubes of a number cancel out the cube root

Let’s now take a step-by-step look at how to use the prime factorization method to find the cube root of 2197.

Determine 2197’s prime factors.

Smallest prime factor that can divide 2197, if we attempt to divide it by any prime number, is 13. Thus, we obtain

2197 = 13 × 13 × 13

Next, group the factors into pairs and express them as cubes.

2197 = (13) = 13³ (From Exponent Law: a^x × a^y = a^x+y)

Now take the cube root and apply it to the expression above, both on the left and right sides.

∛2197 = ∛(13³)

Cube of 13 neutralizes the cube root.

Hence, the cube root of 2197 is 13.

Question: Find cube of 7, will the cube root of the result give 7 again?

Solution: 

Cube of 7 is,

7 × 7 × 7 = 49 × 7 = 343

Cube root of 343 will give 7 back again.

Note: Cube and cube root are co-related and are opposite of each other.

Digit at Unit Place of Cube Root of 2197

In order to find the digit at the unit’s place of the cube root of 2197, the cube root of 2197 is required, however, there are simpler methods that can be used to find the unit’s place value of the cube root of 2197. Prime factorization and Estimation methods are the methods that can be used. In this case, the best-suited method is the Estimation method.

Using Estimation Method to Find Unit Place Value 

• It is important to have the knowledge of the basic cubes and cube roots, that is, the cube and cube roots from 1 to 10,

Numbers	Cubes
1	1
2	8
3	27
4	64
5	125
6	216
7	343
8	512
9	729
10	1000

• 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.