115 LearnersLast updated on May 26th, 2025
Cube Root of 157464
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 157464 and explain the methods used.
What is the Cube Root of 157464?
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, ∛157464 is written as 157464(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 157464, then y³ can be 157464. Since the cube root of 157464 is an exact value, we can write it as 54.
Finding the Cube Root of 157464
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 157464. The common methods we follow to find the cube root are given below:
- Prime factorization method
- Exact cube method
Since 157464 is a perfect cube, we can use the prime factorization method.
Cube Root of 157464 by Prime Factorization
Let's find the cube root of 157464 using the prime factorization method:
First, we perform the prime factorization of 157464:
157464 = 23 × 33 × 73 × 13
Grouping the prime factors in triples, we get:
157464 = (2 × 3 × 7)³ × 13
The cube root is the product of the bases in each group:
∛157464 = 2 × 3 × 7 = 42
However, since 157464 is a perfect cube, this step reveals the calculation error.
Recalculating, the correct prime factorization, we find:
157464 = 54³
Thus, ∛157464 = 54.
Common Mistakes and How to Avoid Them in the Cube Root of 157464
Finding 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
Misidentifying the number as a non-perfect cube.
Children may mistakenly assume that numbers like 157464, which are perfect cubes, are not. They might not recognize that 157464 is 54³. To avoid this error, double-check the prime factorization to confirm if the number is a perfect cube.
Cube Root of 157464 Examples:
Problem 1
Imagine you have a cube-shaped toy that has a total volume of 157464 cubic centimeters. Find the length of one side of the cube.
Side of the cube = ∛157464 = 54 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 54 units.
Problem 2
A company manufactures 157464 cubic meters of material. Calculate the amount of material left after using 12000 cubic meters.
The amount of material left is 145464 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount:
157464 - 12000 = 145464 cubic meters.
Problem 3
A bottle holds 157464 cubic meters of volume. Another bottle holds a volume of 8000 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is 165464 cubic meters.
Explanation
Let’s add the volume of both bottles:
157464 + 8000 = 165464 cubic meters.
Problem 4
When the cube root of 157464 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 54 = 108 The cube of 108 = 1259712
Explanation
When we multiply the cube root of 157464 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(1000000+157464).
∛(1000000+157464) = ∛1157464 ≈ 104.7
Explanation
As shown in the question ∛(1000000+157464), we can simplify that by adding them.
So, 1000000 + 157464 = 1157464.
Then we use this step:
∛1157464 ≈ 104.7 to get the answer.
FAQs on 157464 Cube Root
1.Can we find the Cube Root of 157464?
2.Why is the Cube Root of 157464 a rational number?
3.Is it possible to get the cube root of 157464 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 157464?
8.How do technology and digital tools in United States support learning Algebra and Cube Root of 157464?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Cube Root of 157464
- 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: 54 × 54 × 54 = 157464.
- Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 157464(1/3), ⅓ is the exponent which denotes the cube root of 157464.
- 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, such as 54, which is the cube root of 157464.
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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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