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Last updated on May 26th, 2025

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Cube Root of 0.125

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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 0.125 and explain the methods used.

Cube Root of 0.125 for UK Students
Professor Greenline from BrightChamps

What is the Cube Root of 0.125?

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, ∛0.125 is written as 0.125^(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 0.125, then y^3 can be 0.125. Since 0.125 is a perfect cube, its cube root is exactly 0.5.

Professor Greenline from BrightChamps

Finding the Cube Root of 0.125

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 0.125. 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 0.125, we can use the prime factorization method.

Professor Greenline from BrightChamps

Cube Root of 0.125 by Prime Factorization

Let's find the cube root of 0.125 using the prime factorization method. 0.125 can be expressed as a fraction: 1/8, which is equivalent to 2^(-3) since 8 = 2^3. Therefore, ∛(1/8) = ∛(2^(-3)) = 2^(-1) = 1/2. The cube root of 0.125 is 0.5.

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Common Mistakes and How to Avoid Them in the Cube Root of 0.125

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

Mistake 1

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Trying to find perfect cube roots for non-perfect cube numbers.

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Children sometimes assume all numbers will have an exact whole number as a cube root. For example, they might expect a non-perfect cube to have an exact cube root. To avoid this error, remember that numbers like 0.125 are perfect cubes, and their cube roots can be exact decimals.

Mistake 2

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Ignoring the exponent form

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Most of us might forget the fact that the cube root can also be written in exponent form. For example, forgetting that the cube root of 0.125 is 0.125^(1/3). To avoid this error, always learn the forms in which we can express the cube root of a number.

Mistake 3

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Confusing cube root with division

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Some might mistakenly assume that finding the cube root involves dividing by 3. For example, they might think ∛0.125 is 0.125/3. To avoid this, remember that the cube root is the number that multiplies by itself three times to get 0.125.

Mistake 4

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Using approximation method instead of prime factorization

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Instead of using the prime factorization method for perfect cubes, children might use approximation methods unnecessarily. For example, they might try to estimate the cube root of 0.125 rather than recognizing it as 1/8. Remember that for perfect cubes like 0.125, prime factorization gives an exact result.

Mistake 5

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Rounding too early

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Rounding the cube root too early in the process can lead to errors in subsequent steps. For example, rounding the cube root of 0.125 to 0.1 too early. To avoid this, ensure the whole calculation is done, then round the final result if necessary.

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Cube Root of 0.125 Examples:

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Max, the Girl Character from BrightChamps

Problem 1

Imagine you have a cube-shaped toy that has a total volume of 0.125 cubic meters. Find the length of one side of the toy equal to its cube root.

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Side of the cube = ∛0.125 = 0.5 meters

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 0.5 meters.

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Max, the Girl Character from BrightChamps

Problem 2

A company manufactures 0.125 cubic meters of material. Calculate the amount of material left after using 0.05 cubic meters.

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The amount of material left is 0.075 cubic meters.

Explanation

To find the remaining material, we need to subtract the used material from the total amount: 0.125 - 0.05 = 0.075 cubic meters.

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Max, the Girl Character from BrightChamps

Problem 3

A bottle holds 0.125 cubic meters of volume. Another bottle holds a volume of 0.08 cubic meters. What would be the total volume if the bottles are combined?

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The total volume of the combined bottles is 0.205 cubic meters.

Explanation

Explanation: Let’s add the volume of both bottles: 0.125 + 0.08 = 0.205 cubic meters.

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Max, the Girl Character from BrightChamps

Problem 4

When the cube root of 0.125 is multiplied by 4, calculate the resultant value. How will this affect the cube of the new value?

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4 × 0.5 = 2 The cube of 2 = 8

Explanation

When we multiply the cube root of 0.125 by 4, it results in a number that, when cubed, significantly increases the volume because the cube increases exponentially.

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Max, the Girl Character from BrightChamps

Problem 5

Find ∛(0.25 + 0.25).

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∛(0.25 + 0.25) = ∛0.5 ≈ 0.7937

Explanation

As shown in the question ∛(0.25 + 0.25), we can simplify that by adding them. So, 0.25 + 0.25 = 0.5. Then we use this step: ∛0.5 ≈ 0.7937 to get the answer.

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FAQs on 0.125 Cube Root

1.Can we find the Cube Root of 0.125?

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2.Why is Cube Root of 0.125 rational?

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3.Is it possible to get the cube root of 0.125 as an exact number?

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

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

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6.How does learning Algebra help students in United Kingdom make better decisions in daily life?

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7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Cube Root of 0.125?

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8.How do technology and digital tools in United Kingdom support learning Algebra and Cube Root of 0.125?

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9.Does learning Algebra support future career opportunities for students in United Kingdom?

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Professor Greenline from BrightChamps

Important Glossaries for Cube Root of 0.125

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 or an exact fraction. For example: 0.5 × 0.5 × 0.5 = 0.125, therefore, 0.125 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), 1/3 is the exponent which denotes the cube root of a. Radical sign: The symbol that is used to represent a root which is expressed as (∛). Rational number: A number that can be expressed as a fraction where both numerator and denominator are integers. For example, the cube root of 0.125 is rational because it is 0.5, which equals 1/2.

Professor Greenline from BrightChamps

About BrightChamps inUnited Kingdom

At BrightCHAMPS, we believe algebra is far more than mere symbols it opens the door to countless opportunities! Our mission is to help children throughout the United Kingdom build strong math skills, with today’s focus on the Cube Root of 0.125, placing special emphasis on understanding cube roots in an engaging, enjoyable, and accessible way. Whether your child is working out how fast a roller coaster moves at Alton Towers, keeping score at a local football match, or managing their pocket money for the latest gadgets, mastering algebra gives them confidence for everyday situations. Our interactive lessons are designed to be fun and straightforward. Recognizing that children in the UK learn differently, we adapt our teaching to each child’s individual style. From the bustling streets of London to the picturesque coasts of Cornwall, BrightCHAMPS makes math come alive, exciting learners all over the UK. Let’s make cube roots an enjoyable part of every child’s math journey!
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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.

Max, the Girl Character from BrightChamps

Fun Fact

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

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