115 LearnersLast updated on May 26th, 2025
Cube Root of 681472
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 681472 and explain the methods used.
What is the Cube Root of 681472?
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, ∛681472 is written as 681472(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 681472, then y³ can be 681472. Since the cube root of 681472 is an exact value, we can write it as exactly 88.
Finding the Cube Root of 681472
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 681472. The common methods we follow to find the cube root are given below:
- Prime factorization method
- Approximation method
- Subtraction method
- Halley’s method
Since 681472 is a perfect cube, we can use the prime factorization method.
Cube Root of 681472 by Prime Factorization
Let's find the cube root of 681472 using the prime factorization method.
First, we find the prime factors of 681472:
681472 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 11 × 11 × 11
Grouping the factors in triples, we have: (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (11 × 11 × 11)
Taking one factor from each group, we get: ∛681472 = 2 × 2 × 2 × 11 = 88
The cube root of 681472 is exactly 88.
Common Mistakes and How to Avoid Them in the Cube Root of 681472
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
Trying to find non-integer cube roots for perfect cube numbers.
Children sometimes assume that a perfect cube like 681472 does not have an exact whole number cube root. To avoid this error, memorize that perfect cubes have exact whole number cube roots, like in the case of 681472, which is 88.
Cube Root of 681472 Examples:
Problem 1
Imagine you have a cube-shaped toy that has a total volume of 681472 cubic centimeters. Find the length of one side of the box equal to its cube root.
Side of the cube = ∛681472 = 88 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 88 units.
Problem 2
A company manufactures 681472 cubic meters of material. Calculate the amount of material left after using 200000 cubic meters.
The amount of material left is 481472 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount:
681472 - 200000 = 481472 cubic meters.
Problem 3
A bottle holds 681472 cubic meters of volume. Another bottle holds a volume of 10000 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is 691472 cubic meters.
Explanation
Let’s add the volume of both bottles:
681472 + 10000 = 691472 cubic meters.
Problem 4
When the cube root of 681472 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 88 = 176 The cube of 176 = 5485766
Explanation
When we multiply the cube root of 681472 by 2, it results in a significantly larger cube due to the exponential increase in volume.
Problem 5
Find ∛(400000+281472).
∛(400000 + 281472) = ∛681472 = 88
Explanation
As shown in the question ∛(400000 + 281472), we can simplify that by adding them.
So, 400000 + 281472 = 681472.
Then we use this step: ∛681472 = 88 to get the answer.
FAQs on 681472 Cube Root
1.Can we find the Cube Root of 681472?
2.Why is the Cube Root of 681472 rational?
3.Is it possible to get the cube root of 681472 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?
6.How does learning Algebra help students in Qatar make better decisions in daily life?
7.How can cultural or local activities in Qatar support learning Algebra topics such as Cube Root of 681472?
8.How do technology and digital tools in Qatar support learning Algebra and Cube Root of 681472?
9.Does learning Algebra support future career opportunities for students in Qatar?
Important Glossaries for Cube Root of 681472
- 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: 4 × 4 × 4 = 64, therefore, 64 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 which is expressed as (∛).
- Rational number: A number that can be expressed as a fraction or ratio of two integers. The cube root of 681472 is rational because it is exactly 88.
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About BrightChamps in Qatar
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.
