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Finding the Cube root of 4096 by prime factorisation method

On multiplying a number three times by itself, the resultant number gives us the cube of that number. The number which is multiplied thrice is the cube root of the resultant number. In other words, the cube root is the inverse function of the cube. The symbol of the cube root is ∛. In this article, we are going to discuss the cube root of 4096 using the prime factorisation method.

 

CUBE ROOT OF 4096

The cube root of 4096 is equal to 16. It means that when 16 is multiplied thrice by itself, we get 4096.

 

How to find the cube root?

To find the cube root of a number, we can use the prime factorisation method. By evaluating the prime factors we will make groups of threes of the same values. Then we apply the cube root and the resultant is our answer.

 

How to calculate the cube root of 4096?

Now we will perform the prime factorisation on 4096.

The prime factors of 4096 are 2×2×2×2×2×2×2×2×2×2×2×2.

Total groups of threes of the same values = (2×2×2) × (2×2×2) × (2×2×2) × (2×2×2)

= (23×23×23×23)

Thus, the cube root of 4096 by prime factorization is ∛(2×2×2×2)3 =  ∛163, which is equal to 16.

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Frequently Asked Questions 

Q1. When 4096 is divided by 8, we get the cube of which number.

Sol. The prime factors of 4096 = 23×23×23×23

= 8×8×8×8

When 4096 is divided by 8 = (8×8×8×8)/8

=  8×8×8

= 83 = 512.

Hence, when 4096 is divided by 8, we will get the cube of 8 i.e, 512.

Q2. Is the cube root of 4096 a rational number, whole number or integer?

Ans. The cube root of 4096 is rational because ∛4096 = ∛(2×2×2×2)3=16, and can be expressed in the form of p/(q ) i.e. 16/1 and q is not equal to 0. Therefore, the cube root of 4096 is a rational number.

We know that the set of the whole numbers includes all natural numbers as well as 0 and the set of integers includes all whole numbers as well as their negative counterparts. So, 16 is a whole number and an integer.

Hence,  ∛4096 = 16 is a rational number, whole number and an integer.

Q3. Is 4096 a perfect cube?

Ans. We know that the prime factors of 4096 are 2×2×2×2×2×2×2×2×2×2×2×2. When we form the triplets of 2, we get 23×23×23×23 and after applying the cube root, we get 16 and 16 is an integer. Hence, 4096 is a perfect cube.