Cube Root of 4096

Cube root of 4096 is 16, ∛4096 = 16

The cube root of 4096 is the value that gives the original number when we multiply it three times by itself, and we can write the cube root of 4096 as ∛4096. This is the general meaning for the cube root. If the cube of a is b, then the cube root of b is equal to a. It is easier to find the cube root of a perfect cube number in mathematics. In this article, you will learn what the cube root of 4096 is and how to find the value of the cube root of 4096 using various methods, such as the prime factorisation method, long division method and estimation method, with a step by step procedure.

Learn about cube root in Maths here.

What is the Cube Root of 4096?

As we know, the cube root of the number 4096 is equal to a number that, when multiplied by itself three times, gives the original number 4096. As said above, the cube root of 4096 is represented using the symbol of the 3rd root, such as ∛4096. The cube root of 4096 can be written in various forms as shown below:

How to Find the Cube Root of 4096 Value?

We can find the value of cube root of 4096 using different methods such as:

• Estimation method
• Prime Factorization method
• Long Division method

Let’s learn how to find the Cube Root of 4096 step by step in each of these methods.

Cube Root of 4096 by Estimation method

Go through the steps given below to understand the estimation of the cube root of 4096.

Step 1: First, group the digits from right to left as a group of 3.

(4) (096)

Step 2: Let’s have a look at the cubes of the first 10 numbers.

1³ = 1, 2³ = 8, 3³ = 27, 4³ = 64, 5³ = 125, 6³ = 216, 7³ = 343, 8³ = 512, 9³ = 729, 10³ = 1000.

Here, the unit digit will be 6 when we cube 6.

Step 3: From the previous step, we can say that the cube root of 4096 must contain its unit digit as 6.

Step 4: Now, consider the number 4, it is between 1³ and 2³, i.e. between 1 and 8. Thus, we need to consider the smallest of these two numbers.

So, the cube root of 4096 is 16.

Alternatively, we can estimate the value of cube root of 4096 as follows.

Let p be the number such that the cube of a is 4096, i.e. p³ = 4096.

∛4096 = ∛(p × p × p)

Let us take p = 1, 2, 3,… such that its cube value is equal to 4096.

1 × 1 × 1 = 1

2 × 2 × 2 = 8

3 × 3 × 3 = 27

4 × 4 × 4 = 64

5 × 5 × 5 = 125

….

10 × 10 × 10 = 1000

….

15 × 15 × 15 = 3375

16 × 16 × 16 = 4096

So, ∛4096 = ∛(16 × 16 × 16) = 16

Also, we can conclude that 4096 is a perfect cube since the cube root of 4096 is a whole number.

Cube Root of 4096 by Prime Factorization

Let’s calculate the cube root of 4096 using the prime factorization method.

Step 1: First, write the prime factorization of 4096.

4096 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

Step 2: Now, group these prime factors such that each group contains 3 similar factors.

4096 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2)

Step 3: Take the cube root on both sides and simplify the expression on the right hand side.

∛4096 = ∛[(2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2)]

∛4096 = ∛(2³ × 2³ × 2³ × 2³) = 2 × 2 × 2 × 2 = 16

Therefore, the cube root of 4096 value is 16.

Click here to understand in detail prime factorization.

Cube Root of 4096 upon 5832

In this section, you will learn how to simplify the cube root of 4096/5832.

∛(4096/5832) = ∛4096/ ∛5832

We know that, the cube root of 4096, ∛4096 = 16

And the cube root of 5832, ∛5832 = 18

So, ∛(4096/5832) = 16/18 = 0.888.

Video Lesson on Finding Cube Roots