117 LearnersLast updated on May 26th, 2025
Cube Root of 314432
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 314432 and explain the methods used.
What is the Cube Root of 314432?
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, ∛314432 is written as 314432(1/3). The cube root is just the opposite operation of finding the cube of a number. Since 314432 is a perfect cube, its cube root is an exact whole number, which is 68.
Finding the Cube Root of 314432
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 314432. The common methods we follow to find the cube root are given below:
- Prime factorization method
- Halley’s method
Since 314432 is a perfect cube, we can use the prime factorization method to find its cube root.
Cube Root of 314432 by Prime Factorization
Let's find the cube root of 314432 using the prime factorization method.
First, find the prime factors of 314432: 314432 = 2^8 × 7^3
To find the cube root, take the cube root of the prime factors:
∛314432 = ∛(28 × 73) = 2(8/3) × 7(3/3) = 22 × 71 = 4 × 7 = 28
Thus, the cube root of 314432 is 68.
Common Mistakes and How to Avoid Them in the Cube Root of 314432
Calculating 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
Trying to find non-whole cube roots for perfect cube numbers.
Children often assume that cube roots of large numbers like 314432 are not whole numbers.
For example, they might assume an approximation is necessary when the exact value is 68. To avoid this error, remember that some numbers, like 314432, are perfect cubes and have whole number cube roots.
Cube Root of 314432 Examples:
Problem 1
Imagine you have a cube-shaped toy that has a total volume of 314432 cubic centimeters. Find the length of one side of the cube.
Side of the cube = ∛314432 = 68 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 68 units.
Problem 2
A company manufactures 314432 cubic meters of material. Calculate the amount of material left after using 10000 cubic meters.
The amount of material left is 304432 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount: 314432 - 10000 = 304432 cubic meters.
Problem 3
A container holds 314432 cubic meters of volume. Another container holds a volume of 20000 cubic meters. What would be the total volume if the containers are combined?
The total volume of the combined containers is 334432 cubic meters.
Explanation
Let’s add the volume of both containers: 314432 + 20000 = 334432 cubic meters.
Problem 4
When the cube root of 314432 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 68 = 136 The cube of 136 = 2515456
Explanation
When we multiply the cube root of 314432 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(400000 + 314432).
∛(400000 + 314432) = ∛714432 ≈ 89.2
Explanation
As shown in the question ∛(400000 + 314432), we can simplify that by adding them.
So, 400000 + 314432 = 714432.
Then we use this step: ∛714432 ≈ 89.2 to get the answer.
FAQs on 314432 Cube Root
1.Can we find the Cube Root of 314432?
2.Why is the Cube Root of 314432 rational?
3.Is it possible to get the cube root of 314432 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 India make better decisions in daily life?
7.How can cultural or local activities in India support learning Algebra topics such as Cube Root of 314432?
8.How do technology and digital tools in India support learning Algebra and Cube Root of 314432?
9.Does learning Algebra support future career opportunities for students in India?
Important Glossaries for Cube Root of 314432
- 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, 68 × 68 × 68 = 314432, therefore, 314432 is a perfect cube.
- Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 314432^(1/3), ⅓ is the exponent which denotes the cube root of 314432.
- Radical sign: The symbol that is used to represent a root is expressed as (∛).
- Rational number: A number is rational if it can be expressed as a fraction or a whole number. The cube root of 314432 is rational because it equals 68, a whole number.
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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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