Cube Root of 373248
2026-02-28 11:14 Diff
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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 373248 and explain the methods used.

What is the Cube Root of 373248?

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, ∛373248 is written as 373248(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 373248, then y³ can be 373248. Since the cube root of 373248 is an exact value, we can write it as 72.

Finding the Cube Root of 373248

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 373248. 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, such as 373248, we can use the prime factorization method.

Cube Root of 373248 by Prime Factorization Method

Let's find the cube root of 373248 using the prime factorization method.

First, we factor 373248 into its prime factors: 373248 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3

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

Each group gives us a factor of the cube root: 2 × 2 × 3 × 3 = 72

Therefore, the cube root of 373248 is 72.

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Common Mistakes and How to Avoid Them in the Cube Root of 373248

Finding the perfect cube of a number without any errors can be a difficult task for the 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 storage box that has a total volume of 373248 cubic centimeters. Find the length of one side of the box equal to its cube root.

Okay, lets begin

Side of the cube = ∛373248 = 72 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 72 units.

Well explained 👍

Problem 2

A company produces 373248 cubic meters of material. Calculate the volume left after using 123456 cubic meters.

Okay, lets begin

The volume left is 249792 cubic meters.

Explanation

To find the remaining volume, we need to subtract the used volume from the total volume: 373248 - 123456 = 249792 cubic meters.

Well explained 👍

Problem 3

A container holds 373248 cubic meters of water. Another container holds a volume of 100000 cubic meters. What would be the total volume if the containers are combined?

Okay, lets begin

The total volume of the combined containers is 473248 cubic meters.

Explanation

Let’s add the volume of both containers: 373248 + 100000 = 473248 cubic meters.

Well explained 👍

Problem 4

When the cube root of 373248 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?

Okay, lets begin

2 × 72 = 144 The cube of 144 = 2985984

Explanation

When we multiply the cube root of 373248 by 2, it results in a number that, when cubed, gives 2985984, showing the exponential increase in volume.

Well explained 👍

Problem 5

Find ∛(300000+73248).

Okay, lets begin

∛(300000+73248) = ∛373248 = 72

Explanation

As shown in the question ∛(300000+73248), we can simplify that by adding them.

So, 300000 + 73248 = 373248.

Then we use this step: ∛373248 = 72 to get the answer.

Well explained 👍

FAQs on 373248 Cube Root

1.Can we find the Cube Root of 373248?

Yes, we can find the cube root of 373248 exactly as it is a perfect cube. The cube root of 373248 is exactly 72.

2.Why is the Cube Root of 373248 rational?

The cube root of 373248 is rational because it is an exact whole number, 72, which can be expressed as a ratio of integers.

3.Is it possible to get the cube root of 373248 as an exact number?

Yes, the cube root of 373248 is an exact number. It is 72.

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, such as 373248, which results in an exact whole number.

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 373248

  • 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: 6 × 6 × 6 = 216, therefore, 216 is a perfect cube.
  • Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 373248(1/3), ⅓ is the exponent which denotes the cube root of 373248.
  • Radical sign: The symbol that is used to represent a root which is expressed as (∛).
  • Rational number: Numbers that can be expressed as a ratio of two integers. For example, 72 is a rational number because it can be written as 72/1.

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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.