112 LearnersLast updated on May 26th, 2025
Cube Root of 287496
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 287496 and explain the methods used.
What is the Cube Root of 287496?
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, ∛287496 is written as 287496(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 287496, then y3 can be 287496. Since 287496 is a perfect cube, its cube root is exactly 66.
Finding the Cube Root of 287496
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 287496. 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 perfect cube, we often follow the prime factorization method. Since 287496 is a perfect cube, we can use this method.
Cube Root of 287496 by Prime Factorization
Let's find the cube root of 287496 using the prime factorization method.
First, find the prime factors of 287496: 287496 = 23 × 33 × 113.
Since we want the cube root, we take one factor from each triplet of identical factors:
∛287496 = 2 × 3 × 11 = 66.
The cube root of 287496 is 66.
Common Mistakes and How to Avoid Them in the Cube Root of 287496
Finding the cube root of a number without any errors can be a difficult task for students. This happens for various 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 sometimes mistakenly think that the cube root of a perfect cube like 287496 is not a whole number. However, since 287496 is a perfect cube, its cube root is exactly 66. To avoid this error, confirm that the number is a perfect cube.
Cube Root of 287496 Examples:
Problem 1
Imagine you have a cube-shaped object with a total volume of 287496 cubic centimeters. Find the length of one side of the cube.
Side of the cube = ∛287496 = 66 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 66 units.
Problem 2
A warehouse stores 287496 cubic meters of goods. Calculate the remaining volume if 50000 cubic meters are dispatched.
The remaining volume is 237496 cubic meters.
Explanation
To find the remaining volume, subtract the dispatched goods from the total volume: 287496 - 50000 = 237496 cubic meters.
Problem 3
A tank holds 287496 cubic meters of water. Another tank holds a volume of 120000 cubic meters. What would be the total volume if the tanks are combined?
The total volume of the combined tanks is 407496 cubic meters.
Explanation
To find the total volume, add the volume of both tanks: 287496 + 120000 = 407496 cubic meters.
Problem 4
When the cube root of 287496 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 66 = 132 The cube of 132 = 2299968
Explanation
When we multiply the cube root of 287496 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(50000 + 237496).
∛(50000 + 237496) = ∛287496 = 66
Explanation
As shown in the question ∛(50000 + 237496), we can simplify that by adding them.
So, 50000 + 237496 = 287496.
Then we use this step: ∛287496 = 66 to get the answer.
FAQs on 287496 Cube Root
1.Can we find the Cube Root of 287496?
2.Why is the Cube Root of 287496 rational?
3.Is it possible to get the cube root of 287496 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 287496
- 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 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 is expressed as (∛).
- Rational number: A number that can be expressed as a fraction of two integers. The cube root of 287496 is rational because it is a whole number, 66.
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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.
