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Last updated on April 28th, 2025

Cube Root of 140608

Q: Can we find the Cube Root of 140608?

Yes, we can find the cube root of 140608 exactly as it is a perfect cube. The cube root of 140608 is 52.

Q: Why is Cube Root of 140608 a rational number?

The cube root of 140608 is rational because it results in a whole number: 52.

Q: Is it possible to get the cube root of 140608 as an exact number?

Yes, the cube root of 140608 is an exact number. It is 52.

Q: 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.

Q: 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).

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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 140608 and explain the methods used.

What is the Cube Root of 140608?

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, ∛140608 is written as 140608^(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 140608, then y³ can be 140608. Since the cube root of 140608 is an exact value, we can write it as 52.

$cube root of 140608$

Finding the Cube Root of 140608

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 140608. The common methods we follow to find the cube root are given below:

Prime factorization method
Approximation method
Subtraction method
Halley’s method

Since 140608 is a perfect cube, we can use the prime factorization method to find its cube root.

Cube Root of 140608 by Prime Factorization

Let's find the cube root of 140608 using the prime factorization method.

Step 1: Find the prime factorization of 140608. 140608 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2¹⁴

Step 2: Group the factors in triples since we are finding the cube root. 2¹⁴ = (2⁴) × (2⁴) × (2⁴) × (2²)

Step 3: Take one factor from each group. Cube root = 2^4 = 16

Hence, the cube root of 140608 is 52.

Common Mistakes and How to Avoid Them in the Cube Root of 140608

Cube Root of 140608 Examples:

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Problem 1

Imagine you have a cube-shaped box that has a total volume of 140608 cubic centimeters. Find the length of one side of the box equal to its cube root.

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Explanation

Problem 2

A company manufactures 140608 cubic meters of material. Calculate the amount of material left after using 50000 cubic meters.

Explanation

Problem 3

A bottle holds 52 cubic meters of volume. Another bottle holds a volume of 88 cubic meters. What would be the total volume if the bottles are combined?

Explanation

Problem 4

When the cube root of 140608 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?

Explanation

Problem 5

Find ∛(70000+70608).

Explanation

FAQs on Cube Root of 140608

1.Can we find the Cube Root of 140608?

2.Why is Cube Root of 140608 a rational number?

3.Is it possible to get the cube root of 140608 as an exact number?

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

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

Important Glossaries for Cube Root of 140608

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: 2 × 2 × 2 = 8, therefore, 8 is a perfect cube.
Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In a^(1/3), ⅓ is the exponent which denotes the cube root of a.
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 or a whole number. For example, the cube root of 140608 is rational because it is 52.

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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.