115 LearnersLast updated on May 26th, 2025
Cube Root of 262144
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 262144 and explain the methods used.
What is the Cube Root of 262144?
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, ∛262144 is written as 262144(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 262144, then y3 can be 262144. Since 262144 is a perfect cube, its cube root is exactly 64.
Finding the Cube Root of 262144
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 262144. 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 number like 262144, we often use the prime factorization method or direct calculation. Since 262144 is a perfect cube, we can easily find its cube root using straightforward calculations.
Cube Root of 262144 by Prime Factorization
Let's find the cube root of 262144 using the prime factorization method.
The prime factorization of 262144 is 2^18.
We can group the factors in triples of three identical numbers: (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2)
This gives us (23)6 = 643.
Thus, the cube root of 262144 is 64.
Common Mistakes and How to Avoid Them in the Cube Root of 262144
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 the students commonly make and the ways to avoid them:
Mistake 1
Trying to find non-perfect cube roots for perfect cube numbers.
Children sometimes try to calculate an approximate value for the cube root of numbers like 262144, which are perfect cubes.
For example, they assume that they need to find a decimal approximation for 262144 when it’s actually a perfect cube. To avoid this error, recognize that some numbers have an exact cube root, that is, the cube root of 262144 is exactly 64.
Cube Root of 262144 Examples:
Problem 1
Imagine you have a cube-shaped storage container that has a total volume of 262144 cubic centimeters. Find the length of one side of the cube.
Side of the cube = ∛262144 = 64 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 64 units.
Problem 2
A storage facility has a cubic volume of 262144 cubic meters. Calculate how many smaller cubes with a side length of 32 meters can fit inside.
The number of smaller cubes that can fit inside is 8.
Explanation
The volume of one smaller cube is 32^3 = 32768 cubic meters.
The number of such smaller cubes that can fit inside is 262144 / 32768 = 8.
Problem 3
A company produces 262144 cubic meters of material. Calculate the amount of material left after using 100000 cubic meters.
The amount of material left is 162144 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount: 262144 - 100000 = 162144 cubic meters.
Problem 4
A storage box holds a volume of 262144 cubic meters. Another storage box holds a volume of 32768 cubic meters. What would be the total volume if the boxes are combined?
The total volume of the combined boxes is 294912 cubic meters.
Explanation
Let’s add the volume of both boxes: 262144 + 32768 = 294912 cubic meters.
Problem 5
Find ∛(100000 + 162144).
∛(100000 + 162144) = ∛262144 = 64
Explanation
As shown in the question ∛(100000 + 162144), we can simplify that by adding them.
So, 100000 + 162144 = 262144.
Then we use this step: ∛262144 = 64 to get the answer.
FAQs on 262144 Cube Root
1.Can we find the Cube Root of 262144?
2.Why is Cube Root of 262144 a rational number?
3.Is it possible to get the cube root of 262144 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 Kingdom make better decisions in daily life?
7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Cube Root of 262144?
8.How do technology and digital tools in United Kingdom support learning Algebra and Cube Root of 262144?
9.Does learning Algebra support future career opportunities for students in United Kingdom?
Important Glossaries for Cube Root of 262144
- 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. For example, 4 × 4 × 4 = 64, therefore, 64 is a perfect cube.
- Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 262144^(1/3), ⅓ is the exponent which denotes the cube root.
- 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 the quotient of two integers, and the cube root of a perfect cube like 262144 is rational because it is a whole number.
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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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