143 LearnersLast updated on May 26th, 2025
Cube Root of 1157625
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 1157625 and explain the methods used.
What is the Cube Root of 1157625?
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, ∛1157625 is written as 1157625(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 1157625, then y³ = 1157625. Since the cube root of 1157625 is an exact value, it is 105.
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Finding the Cube Root of 1157625
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 1157625. The common methods we follow to find the cube root are given below:
- Prime factorization method
- Approximation method
- Subtraction method
- Halley’s method
Since 1157625 is a perfect cube, we can use the prime factorization method to find its cube root.
Cube Root of 1157625 by Prime Factorization Method
Let's find the cube root of 1157625 using the prime factorization method.
First, we find the prime factors of 1157625: 1157625 = 3 × 3 × 3 × 5 × 5 × 5 × 7 × 7 × 7
Pair the prime factors in triples: (3 × 3 × 3) × (5 × 5 × 5) × (7 × 7 × 7)
The cube root is: ∛1157625 = 3 × 5 × 7 = 105
Common Mistakes and How to Avoid Them in the Cube Root of 1157625
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 approximate cube roots for perfect cube numbers.
Children sometimes try to approximate the cube root of numbers like 1157625, which are perfect cubes. To avoid this error, remember that some numbers have an exact cube root, and for 1157625, it is exactly 105.
Mistake 2
Ignoring the exponent form
Most of us might forget the fact that the cube root can also be written in exponent form.
For example: Forgetting that the cube root of 1157625 can be written as 1157625^(1/3). To avoid this error, always learn the forms in which we can express the cube root of a number.
Mistake 3
Confusing cube root with division
To avoid this, children should remember that the cube root of 1157625 is the number they multiply by itself three times to get 1157625, not by dividing 1157625 by 3.
Mistake 4
Using approximation instead of prime factorization for perfect cubes
Instead of using the prime factorization method for perfect cubes, children end up using approximation methods.
For example, they might try to find the cube root of 1157625 using approximation. Remember that prime factorization is the best method for perfect cubes.
Mistake 5
Rounding too early
Rounding the cube root too early in the process can lead to errors in the subsequent steps.
For example, we might round the cube root of a non-perfect cube number too early in the calculation. To avoid this error, ensure the whole calculation is done, then round the final result if necessary.
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Cube Root of 1157625 Examples:
Problem 1
Imagine you have a cube-shaped container that has a total volume of 1157625 cubic centimeters. Find the length of one side of the cube equal to its cube root.
Side of the cube = ∛1157625 = 105 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 105 units.
Problem 2
A company manufactures 1157625 cubic meters of material. Calculate the amount of material left after using 105000 cubic meters.
The amount of material left is 1052625 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount: 1157625 - 105000 = 1052625 cubic meters.
Problem 3
A bottle holds 1157625 cubic meters of volume. Another bottle holds a volume of 210000 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is 1367625 cubic meters.
Explanation
Let’s add the volume of both bottles: 1157625 + 210000 = 1367625 cubic meters.
Problem 4
When the cube root of 1157625 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 105 = 210 The cube of 210 = 9261000
Explanation
When we multiply the cube root of 1157625 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(1157625 + 1157625).
∛(1157625 + 1157625) = ∛2315250 ≈ 132.09
Explanation
As shown in the question ∛(1157625 + 1157625), we can simplify that by adding them. So, 1157625 + 1157625 = 2315250. Then we use this step: ∛2315250 ≈ 132.09 to get the answer.
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FAQs on 1157625 Cube Root
1.Can we find the Cube Root of 1157625 exactly?
2.Why is Cube Root of 1157625 rational?
3.Is it possible to get the cube root of 1157625 as an approximate 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 1157625?
8.How do technology and digital tools in India support learning Algebra and Cube Root of 1157625?
9.Does learning Algebra support future career opportunities for students in India?
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Important Glossaries for Cube Root of 1157625
- 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: 105 × 105 × 105 = 1157625, therefore, 1157625 is a perfect cube.
- Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 1157625(1/3), ⅓ is the exponent which denotes the cube root of 1157625.
- Radical sign: The symbol that is used to represent a root is expressed as (∛).
- Rational number: A number that can be expressed as a ratio of two integers, where the denominator is not zero. The cube root of 1157625 is rational because it is exactly 105.
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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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