Cube Root of 4741632
2026-02-21 20:56 Diff
https://brightchamps.com/en-us/math/algebra/cube-root-of-4741632

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Last updated on August 5, 2025

A number we multiply by itself three times to get the original number is its cube root. It has various uses in real life, such as finding the volume of cube-shaped objects and designing structures. We will now find the cube root of 4741632 and explain the methods used.

What is the Cube Root of 4741632?

We have learned the definition of the cube root. Now, let’s learn how it is represented using a symbol and exponent. The symbol we use to express the cube root is the radical sign (∛), and the exponent we use is ⅓. In exponential form, ∛4741632 is written as 4741632(1/3).

The cube root is just the opposite operation of finding the cube of a number. For example: Assume ‘y’ as the cube root of 4741632, then y³ can be 4741632. Since the cube root of 4741632 is an exact value, it can be written as 168.

Finding the Cube Root of 4741632

Finding the cube root of a number is to identify the number that must be multiplied three times resulting in the target number. Now, we will go through the different ways to find the cube root of 4741632. The common methods we follow to find the cube root are given below:

  • Prime factorization method
  • Approximation method
  • Subtraction method
  • Halley’s method

To find the cube root of a perfect cube number like 4741632, we can use the prime factorization method.

Cube Root of 4741632 by Prime Factorization Method

Let's find the cube root of 4741632 using the prime factorization method.

First, we find the prime factors: 4741632 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 13 × 13 × 13

Group the prime factors into triples: (2 × 2 × 2) × (2 × 2 × 2) × (3 × 3 × 3) × (13 × 13 × 13)

Take one factor from each group: 2 × 2 × 3 × 13 = 168

Thus, the cube root of 4741632 is exactly 168.

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Common Mistakes and How to Avoid Them in the Cube Root of 4741632

Finding the cube root of a number without any errors can be a difficult task for students. This happens for many reasons. Here are a few mistakes the students commonly make and the ways to avoid them:

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Problem 1

Imagine you have a cube-shaped toy that has a total volume of 4741632 cubic centimeters. Find the length of one side of the cube equal to its cube root.

Okay, lets begin

Side of the cube = ∛4741632 = 168 units

Explanation

To find the side of the cube, we need to find the cube root of the given volume. Therefore, the side length of the cube is exactly 168 units.

Well explained 👍

Problem 2

A company manufactures 4741632 cubic meters of material. Calculate the amount of material left after using 1632 cubic meters.

Okay, lets begin

The amount of material left is 4740000 cubic meters.

Explanation

To find the remaining material, we need to subtract the used material from the total amount: 4741632 - 1632 = 4740000 cubic meters.

Well explained 👍

Problem 3

A bottle holds 4741632 cubic meters of volume. Another bottle holds a volume of 8 cubic meters. What would be the total volume if the bottles are combined?

Okay, lets begin

The total volume of the combined bottles is 4741640 cubic meters.

Explanation

Explanation: Let’s add the volume of both bottles: 4741632 + 8 = 4741640 cubic meters.

Well explained 👍

Problem 4

When the cube root of 4741632 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?

Okay, lets begin

2 × 168 = 336 The cube of 336 = 3796416

Explanation

When we multiply the cube root of 4741632 by 2, it results in a significant increase in the volume because the cube increases exponentially.

Well explained 👍

Problem 5

Find ∛(4741632 + 8).

Okay, lets begin

∛(4741632 + 8) = ∛4741640 ≈ 168.002

Explanation

As shown in the question ∛(4741632 + 8), we can simplify that by adding them. So, 4741632 + 8 = 4741640. Then we use this step: ∛4741640 ≈ 168.002 to get the answer.

Well explained 👍

FAQs on 4741632 Cube Root

1.Can we find the Cube Root of 4741632?

Yes, we can find the cube root of 4741632 exactly as the cube root of 4741632 is a whole number. It is exactly 168.

2.Why is the Cube Root of 4741632 rational?

The cube root of 4741632 is rational because it results in a whole number, which can be expressed as a fraction (168/1).

3.Is it possible to get the cube root of 4741632 as an exact number?

Yes, the cube root of 4741632 is an exact number. It is 168.

4.Can we find the cube root of any number using prime factorization?

The prime factorization method can be used to calculate the cube root of perfect cube numbers. For example, 2 × 2 × 2 = 8, so 8 is a perfect cube.

5.Is there any formula to find the cube root of a number?

Yes, the formula we use for the cube root of any number ‘a’ is a^(1/3).

Important Glossaries for Cube Root of 4741632

  • Cube root: The number that is multiplied three times by itself to get the given number is the cube root of that number.
  • Perfect cube: A number is a perfect cube when it is the product of multiplying a number three times by itself. A perfect cube always results in a whole number. For example: 168 × 168 × 168 = 4741632, therefore, 4741632 is a perfect cube.
  • Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 4741632(1/3), ⅓ is the exponent that denotes the cube root of 4741632.
  • Radical sign: The symbol that is used to represent a root is expressed as (∛).
  • Rational number: A number that can be expressed as a fraction of two integers, such as 168, which is the cube root of 4741632.

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Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.