110 LearnersLast updated on May 26th, 2025
Cube Root of 10648
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 10648 and explain the methods used.
What is the Cube Root of 10648?
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, ∛10648 is written as 10648(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 10648, then y3 can be 10648. Since 10648 is a perfect cube, we can find its cube root exactly as 22.
Finding the Cube Root of 10648
Finding the cube root of a number involves identifying the number that, when multiplied by itself three times, results in the target number. Now, we will go through the different ways to find the cube root of 10648. The common methods we follow to find the cube root are given below:
- Prime factorization method
- Subtraction method
- Approximation method
- Halley’s method
Since 10648 is a perfect cube, we can use the prime factorization method or simple calculation to find the cube root accurately.
Cube Root of 10648 by Prime Factorization
Let's find the cube root of 10648 using the prime factorization method.
First, we find the prime factors of 10648:
10648 = 2 × 2 × 2 × 11 × 11 × 11
Grouping the prime factors in triples:
10648 = (2 × 2 × 2) × (11 × 11 × 11)
= 23 × 113
Taking the cube root of both sides, we get: ∛10648 = 2 × 11 = 22
The cube root of 10648 is exactly 22.
Common Mistakes and How to Avoid Them in the Cube Root of 10648
Finding the perfect cube root of a number without any errors can be a challenging task for students. This happens for many reasons. Here are a few mistakes students commonly make and how to avoid them:
Mistake 1
Trying to find approximate cube roots for perfect cube numbers.
Students sometimes try to approximate cube roots for numbers like 10648, which are perfect cubes.
For example: They might mistakenly think they need to approximate instead of calculating exactly. To avoid this error, remember that for perfect cubes, the cube root will be an exact whole number. For 10648, the cube root is exactly 22.
Cube Root of 10648 Examples:
Problem 1
Imagine you have a cube-shaped toy that has a total volume of 10648 cubic centimeters. Find the length of one side of the box equal to its cube root.
Side of the cube = ∛10648 = 22 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 22 units.
Problem 2
A company manufactures 10648 cubic meters of material. Calculate the amount of material left after using 6000 cubic meters.
The amount of material left is 4648 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount:
10648 - 6000 = 4648 cubic meters.
Problem 3
A bottle holds 10648 cubic meters of volume. Another bottle holds a volume of 352 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is 11000 cubic meters.
Explanation
Let’s add the volume of both bottles:
10648 + 352 = 11000 cubic meters.
Problem 4
When the cube root of 10648 is multiplied by 3, calculate the resultant value. How will this affect the cube of the new value?
3 × 22 = 66 The cube of 66 = 287496
Explanation
When we multiply the cube root of 10648 by 3, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(5300 + 5348).
∛(5300 + 5348) = ∛10648 = 22
Explanation
As shown in the question ∛(5300 + 5348), we can simplify that by adding them.
So, 5300 + 5348 = 10648.
Then we use this step: ∛10648 = 22 to get the answer.
FAQs on 10648 Cube Root
1.Can we find the Cube Root of 10648?
2.Why is the Cube Root of 10648 rational?
3.Is it possible to get the cube root of 10648 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 United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Cube Root of 10648?
8.How do technology and digital tools in United States support learning Algebra and Cube Root of 10648?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Cube Root of 10648
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 10648(1/3), ⅓ is the exponent which denotes the cube root of 10648.
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 of two integers is a rational number. The cube root of 10648 is rational because it is 22.
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Jaskaran Singh Saluja
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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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