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Last updated on May 26th, 2025

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Cube Root of -2744

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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 -2744 and explain the methods used.

Cube Root of -2744 for Indian Students
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What is the Cube Root of -2744?

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, ∛-2744 is written as (-2744)^(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 -2744, then y³ can be -2744. Since the cube root of -2744 is an exact value, we can write it as -14.

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Finding the Cube Root of -2744

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 -2744. 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 like -2744, we can use the prime factorization method.

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Cube Root of -2744 by Prime Factorization

Let's find the cube root of -2744 using the prime factorization method. First, we factorize -2744: -2744 = -2 × 2 × 2 × 7 × 7 × 7. Since we have three 2s and three 7s, we can group them as: (-2 × 7) × (2 × 7) × (2 × 7) = (-14) × 14 × 14. Therefore, the cube root of -2744 is -14.

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Common Mistakes and How to Avoid Them in the Cube Root of -2744

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:

Mistake 1

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

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Children sometimes try to calculate an exact whole number for the cube root of numbers that are not perfect cubes. However, -2744 is a perfect cube. To avoid errors, recognize that some numbers like -2744 do have a perfect cube root, which is -14.

Mistake 2

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Ignoring the exponent form

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Most of us might forget the fact that cube roots can also be written in exponent form. For example: Forgetting that the cube root of -2744 is (-2744)^(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 may mistakenly assume that finding the cube root of -2744 involves dividing -2744 by 3. To avoid this, remember that the cube root of -2744 is the number that, when multiplied by itself three times, equals -2744.

Mistake 4

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Using approximation instead of prime factorization for perfect cubes

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Instead of using the prime factorization method for perfect cubes, children might use approximation. For perfect cubes like -2744, use the prime factorization method to find the exact cube root, which is -14.

Mistake 5

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Misinterpreting negative values

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Rounding errors might occur when students misinterpret negative values. For example, they might incorrectly round the cube root of -2744 to a positive value. To avoid this, remember that the cube root of a negative number is negative.

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Cube Root of -2744 Examples:

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Problem 1

Imagine you have a cube-shaped box with a total volume of -2744 cubic centimeters. Find the length of one side of the box equal to its cube root.

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Side of the cube = ∛-2744 = -14 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 -14 units.

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Problem 2

A company removed -2744 cubic meters of material from a site. Calculate the amount of material added back if 2000 cubic meters were replaced.

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The amount of material added back is 2000 cubic meters.

Explanation

To find the remaining material added back, we consider the addition of 2000 cubic meters to the removed material.

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Problem 3

A container holds -2744 cubic meters of volume. If additional material of 500 cubic meters is added, what would be the new total volume?

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The new total volume of the container is -2244 cubic meters.

Explanation

Explanation: Let’s add the volume of additional material to the container: -2744 + 500 = -2244 cubic meters.

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Problem 4

When the cube root of -2744 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?

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2 × -14 = -28 The cube of -28 = -21952

Explanation

When we multiply the cube root of -2744 by 2, it results in a significant increase in the volume because the cube increases exponentially.

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Problem 5

Find ∛(-500 + 244).

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∛(-500 + 244) = ∛-256 = -6.3496

Explanation

As shown in the question ∛(-500 + 244), we can simplify that by adding them. So, -500 + 244 = -256. Then we use this step: ∛-256 ≈ -6.3496 to get the answer.

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FAQs on Cube Root of -2744

1.Can we find the Cube Root of -2744?

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2.Why is Cube Root of -2744 rational?

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3.Is it possible to get the cube root of -2744 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 India make better decisions in daily life?

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7.How can cultural or local activities in India support learning Algebra topics such as Cube Root of -2744?

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8.How do technology and digital tools in India support learning Algebra and Cube Root of -2744?

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

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Important Glossaries for Cube Root of -2744

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, (-14) × (-14) × (-14) = -2744, therefore, -2744 is a perfect cube. Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In (-2744)^(1/3), ⅓ is the exponent which denotes the cube root of -2744. Radical sign: The symbol that is used to represent a root, expressed as (∛). Rational number: A number that can be expressed as a fraction or a whole number. The cube root of -2744 is rational because it is -14.

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About BrightChamps in India

At BrightChamps, we understand algebra goes beyond symbols—it’s a pathway to limitless opportunities! Our mission is to help children throughout India master vital math skills, with today’s focus on the Cube Root of -2744 and a special emphasis on grasping cube roots—in a way that’s engaging, enjoyable, and easy to follow. Whether your child is calculating the speed of a passing train, keeping track of scores during a cricket match, or managing pocket money for the latest gadgets, mastering algebra builds the confidence needed for everyday life. Our interactive lessons ensure learning is simple and fun. Aware that children in India learn in various ways, we tailor our teaching to each child’s unique style. From the busy markets of Mumbai to the vibrant streets of Delhi, BrightChamps makes math relatable and exciting all over India. Let’s make cube roots a fun 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.

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Fun Fact

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

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