109 LearnersLast updated on May 26th, 2025
Cube Root of 140608
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 140608 and explain the methods used.
What is the Cube Root of 140608?
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, ∛140608 is written as 140608(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 140608, then y3 can be 140608. Since the cube root of 140608 is an exact value, we can write it as 52.
Finding the Cube Root of 140608
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 140608. The common methods we follow to find the cube root are given below:
- Prime factorization method
- Approximation method
- Subtraction method
- Halley’s method
Since 140608 is a perfect cube, we can use the prime factorization method to find its cube root.
Cube Root of 140608 by Prime Factorization
Let's find the cube root of 140608 using the prime factorization method.
Step 1: Find the prime factorization of 140608. 140608 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 214
Step 2: Group the factors in triples since we are finding the cube root. 214 = (24) × (24) × (24) × (22)
Step 3: Take one factor from each group. Cube root = 2^4 = 16
Hence, the cube root of 140608 is 52.
Common Mistakes and How to Avoid Them in the Cube Root of 140608
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
Confusing cube roots for non-perfect cube numbers.
Children might confuse the process of finding cube roots for perfect and non-perfect cubes.
For example, they might think that all numbers have non-exact cube roots like 39. To avoid this error, practice with both perfect and non-perfect cubes. Remember that the cube root of 140608 is exactly 52.
Cube Root of 140608 Examples:
Problem 1
Imagine you have a cube-shaped box that has a total volume of 140608 cubic centimeters. Find the length of one side of the box equal to its cube root.
Side of the cube = ∛140608 = 52 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 52 units.
Problem 2
A company manufactures 140608 cubic meters of material. Calculate the amount of material left after using 50000 cubic meters.
The amount of material left is 90608 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount:
140608 - 50000 = 90608 cubic meters.
Problem 3
A bottle holds 52 cubic meters of volume. Another bottle holds a volume of 88 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is 140 cubic meters.
Explanation
Let’s add the volume of both bottles:
52 + 88 = 140 cubic meters.
Problem 4
When the cube root of 140608 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 52 = 104 The cube of 104 = 1124864
Explanation
When we multiply the cube root of 140608 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(70000+70608).
∛(70000+70608) = ∛140608 = 52
Explanation
As shown in the question ∛(70000+70608), we can simplify that by adding them.
So, 70000 + 70608 = 140608.
Then we use this step:
∛140608 = 52 to get the answer.
FAQs on Cube Root of 140608
1.Can we find the Cube Root of 140608?
2.Why is Cube Root of 140608 a rational number?
3.Is it possible to get the cube root of 140608 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 Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Cube Root of 140608?
8.How do technology and digital tools in Australia support learning Algebra and Cube Root of 140608?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for Cube Root of 140608
- 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 or a whole number. For example, the cube root of 140608 is rational because it is 52.
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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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