126 LearnersLast updated on May 26th, 2025
Cube Root of 748
A number that, when multiplied by itself three times, gives the original number is its cube root. It has various applications in real life, such as determining the volume of cube-shaped objects and in architectural design. We will now find the cube root of 748 and explain the methods used.
What is the Cube Root of 748?
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, ∛748 is written as 748(1/3). The cube root is just the opposite operation of finding the cube of a number. For example, assume ‘y’ is the cube root of 748, then y3 can be 748. Since the cube root of 748 is not an exact value, we can write it as approximately 9.0807.
Finding the Cube Root of 748
Finding the cube root of a number involves identifying the number that must be multiplied three times to result in the target number. Now, we will go through different ways to find the cube root of 748. The common methods we use 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 non-perfect number, we often follow Halley’s method. Since 748 is not a perfect cube, we use Halley’s method.
Cube Root of 748 by Halley’s method
Let's find the cube root of 748 using Halley’s method. The formula is: ∛a ≅ x((x3 + 2a) / (2x3 + a))
where: a = the number for which the cube root is being calculated
x = the nearest perfect cube
Substituting,
a = 748;
x = 9
∛a ≅ 9((93 + 2 × 748) / (2 × 93 + 748))
∛748 ≅ 9((729 + 2 × 748) / (2 × 729 + 748))
∛748 ≅ 9.0807
The cube root of 748 is approximately 9.0807.
Common Mistakes and How to Avoid Them in the Cube Root of 748
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 ways to avoid them:
Mistake 1
Trying to find perfect cube roots for non-perfect cube numbers.
Children often try to calculate an exact whole number for the cube root of numbers like 748, which are not perfect cubes.
For example, they assume they would get an exact whole number for 748 like they do for 729 (since 729 is a perfect cube). To avoid this error, remember that some numbers don't have a perfect cube root; the cube root of 748 is approximately 9.0807.
Cube Root of 748 Examples:
Problem 1
Imagine you have a cube-shaped container with a total volume of 748 cubic centimeters. Find the length of one side of the cube, equal to its cube root.
Side of the cube = ∛748 ≈ 9.08 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 approximately 9.08 units.
Problem 2
A company manufactures 748 cubic meters of a material. Calculate the amount of material left after using 300 cubic meters.
The amount of material left is 448 cubic meters.
Explanation
To find the remaining material, subtract the used material from the total amount:
748 - 300 = 448 cubic meters.
Problem 3
A storage tank holds 748 cubic meters of water. Another tank holds a volume of 100 cubic meters. What would be the total volume if the tanks are combined?
The total volume of the combined tanks is 848 cubic meters.
Explanation
Explanation: Let’s add the volume of both tanks:
748 + 100 = 848 cubic meters.
Problem 4
When the cube root of 748 is multiplied by 3, calculate the resultant value. How will this affect the cube of the new value?
3 × 9.08 ≈ 27.24 The cube of 27.24 ≈ 20,231.24
Explanation
When multiplying the cube root of 748 by 3, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(375 + 373).
∛(375 + 373) = ∛748 ≈ 9.08
Explanation
As shown in the question ∛(375 + 373), we can simplify that by adding them.
So, 375 + 373 = 748.
Then we use this step: ∛748 ≈ 9.08 to get the answer.
FAQs on 748 Cube Root
1.Can we find the Cube Root of 748?
2.Why is the Cube Root of 748 irrational?
3.Is it possible to get the cube root of 748 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 748
- 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, 3 × 3 × 3 = 27; therefore, 27 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, expressed as (∛).
- Irrational number: Numbers that cannot be expressed as a simple fraction are irrational. For example, the cube root of 748 is irrational because its decimal form goes on continuously without repeating numbers.
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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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
