Question

A) use three strategies to determine ∛2197

B) which strategy you prefer to use. why?

Answer 1

13

Explanation:

Let us now calculate the cube root of 2197 by using the estimation method in a step-by-step manner.

1. Consider the digit given at the unit’s place of 2197. The unit place 2197 has 7.

2. Look at the cubes table given above. In the cube table, check the cube of which number has digit 7 at the unit’s place.

Clearly, we can see 3³ = 27.

It implies that the unit digit of the cube root of 2197 is 3.

3. Now to calculate the tenth place of the cube root of 2197, we will overlook the last 3 digits of 2197, i.e., 197. Considering 2 as a benchmark figure, we can see that the digit 2 falls between 1³ and 2³, i.e., between 1 and 8. Here, we will consider the lowest numbers closest to 2

which is 1. As 1³ = 1. Hence, the tenth place of the cube root of 2197

is 1. Hence, the cube root of 2197 is 13.

Cube Root of 2197 by Prime Factorization Method

Here, we will discuss about the prime factorization method to determine the prime factors of 2197. After determining the prime

factors of 2197, we will pair the factors in a group of three and write them as cubes. As the cubes of a number neutralise the cube root, we will get the desired value. Now let us learn how to find the cube root of 2197 by the prime factorization method in a step-by-step manner.

1. Calculate the prime factors of 2197.

If we try to divide 2197 by any prime number, we will find

that the smallest prime factor which can divide 2197 is

13. Hence, we get

2197 = 13 * 13 * 13

2. Now pair the factors in a group of 3 and express them in the

form of cubes.

2197 = (13) = 13³ (As we know exponent law: a x × a y =

a x + y )

3. Now apply cube root to both left and right sides of the above

expression.

=

The cube root gets neutralised by the cube of 13.

Hence, the cube root of 2197 is 13.

i prefer FACTORIZATION METHOD

I HOPE THIS HELPED

Answer 2

A) There are a few different strategies that can be used to determine ∛2197:

The first strategy is to use a calculator to find the value of ∛2197 directly. This is the easiest and quickest method, but it requires access to a calculator with a cube root function.
The second strategy is to use the property of radicals that says ∛a * ∛b = ∛(ab), which means that we can find ∛2197 by finding the cube root of each prime factor of 2197 and then multiplying the results together. For example, we can write 2197 as 713*19, so ∛2197 = ∛7 * ∛13 * ∛19 = 7^(1/3) * 13^(1/3) * 19^(1/3).
The third strategy is to use the binomial theorem, which says that (a+b)^n = a^n + n*a^(n-1)b + ... + b^n for any positive integer n. We can use this theorem to expand (∛2)^6, which equals (∛2)^(32) = (∛2)^3 * (∛2)^3 = ∛2197.
B) Personally, I prefer to use the second strategy, which involves finding the prime factorization of 2197 and then taking the cube root of each factor. This method is relatively simple and straightforward, and it doesn't require a calculator or advanced mathematical knowledge. It also allows us to check our work by verifying that the result is a perfect cube, which means that it can be written in the form a^3 for some integer a. In this case, the result is 7 * 13 * 19, which can be written as 3^3 * 13^3, so we know that our answer is correct.