152 LearnersLast updated on May 26th, 2025
Cube Root of 749
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 dimensions of cube-shaped objects and designing structures. We will now explore the cube root of 749 and explain the methods used to find it.
What is the Cube Root of 749?
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, ∛749 is written as 749(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 749, then y3 can be 749. Since the cube root of 749 is not an exact value, we can write it as approximately 9.0802.
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Finding the Cube Root of 749
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 the different ways to find the cube root of 749. 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 non-perfect number like 749, we often follow Halley’s method.
Cube Root of 749 by Halley’s Method
Let's find the cube root of 749 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 = 749;
x = 9
∛a ≅ 9((93 + 2 × 749) / (2 × 93 + 749))
∛749 ≅ 9((729 + 2 × 749) / (2 × 729 + 749))
∛749 ≅ 9.0802
The cube root of 749 is approximately 9.0802.
Common Mistakes and How to Avoid Them in the Cube Root of 749
Finding the cube root of a number without any errors can be a challenging task. This happens for many reasons. Here are a few mistakes commonly made and ways to avoid them:
Mistake 1
Trying to find perfect cube roots for non-perfect cube numbers.
People often try to calculate an exact whole number for the cube root of numbers like 749, which are not perfect cubes.
For instance, they may assume they would get an exact whole number for 749 like they get for 729 (since ∛729 = 9). To avoid this error, remember that some numbers don't have a perfect cube root; the cube root of 749 is approximately 9.0802.
Mistake 2
Ignoring the exponent form
Many might forget that the cube root can also be written in exponent form.
For example: Forgetting that the cube root of 749 is 749^(1/3). To avoid this error, always learn the forms in which we can express the cube root of a number.
Mistake 3
Confusing cube root with division
Assuming the cube root of 749 is to divide 749 by 3 is a common mistake. To avoid this, remember that the cube root of 749 is the number that, when multiplied by itself three times, equals 749.
Mistake 4
Using prime factorization instead of Halley’s method
Instead of using Halley’s method for non-perfect cubes, some might try using prime factorization.
For example, they might attempt to find the cube root of 749 by breaking it down into its prime factors. Remember that prime factorization can help analyze a number's factors, but it's not the best method for non-perfect cubes. Since 749 is a non-perfect cube, you can use either the approximation method or Halley’s method.
Mistake 5
Rounding too early
Rounding the cube root too early in the process can lead to errors in subsequent steps.
For example, one might round the cube root of 749 to 9.1 too early in the calculation. To avoid this, ensure the entire calculation is done, then round the final result.
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Cube Root of 749 Examples:
Problem 1
Imagine you have a cube-shaped container that has a total volume of 749 cubic centimeters. Find the length of one side of the cube equal to its cube root.
Side of the cube = ∛749 ≈ 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 749 cubic meters of material. Calculate the amount of material left after using 300 cubic meters.
The amount of material left is 449 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount:
749 - 300 = 449 cubic meters.
Problem 3
A bottle holds 749 cubic meters of volume. Another bottle holds a volume of 150 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is 899 cubic meters.
Explanation
Let’s add the volume of both bottles:
749 + 150 = 899 cubic meters.
Problem 4
When the cube root of 749 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 9.08 ≈ 18.16 The cube of 18.16 ≈ 5980.2
Explanation
When we multiply the cube root of 749 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(375 + 374).
∛(375 + 374) = ∛749 ≈ 9.08
Explanation
As shown in the question ∛(375 + 374), we can simplify that by adding them.
So, 375 + 374 = 749.
Then we use this step: ∛749 ≈ 9.08 to get the answer.
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FAQs on 749 Cube Root
1.Can we find the Cube Root of 749?
2.Why is Cube Root of 749 irrational?
3.Is it possible to get the cube root of 749 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 749?
8.How do technology and digital tools in Qatar support learning Algebra and Cube Root of 749?
9.Does learning Algebra support future career opportunities for students in Qatar?
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Important Glossaries for Cube Root of 749
- Cube root: The number that, when multiplied three times by itself, yields 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 a^(1/3), 1/3 is the exponent which denotes the cube root.
- Radical sign: The symbol used to represent a root is expressed as (∛).
- Irrational number: Numbers that cannot be expressed as a simple fraction are irrational. For example, the cube root of 749 is irrational because its decimal form goes on continuously without repeating.
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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.
