265 LearnersLast updated on May 26th, 2025
Cube Root Of 432
The cube root of a number is a value that when multiplied by itself three times gives back the original number. We apply the function of cube roots in the fields of engineering, designing, financial mathematics, and many more. Let's learn more about the cube root of 432.
What is The Cube Root Of 432?
The cube root can be classified into two categories: perfect cubes and non-perfect cubes. For example, the cube root of 512 is 8 which is a whole number, making it a perfect cube. However, the cube root of 432 is not a whole number. The cube root of 432 is approximately 7.559526299.
The cube root of 432 is represented using the radical sign as ∛432, and can also be written in exponential form as 4321/3. The prime factorization of 432 is 24 × 33. It is also an irrational number where ∛432 cannot be expressed in the form of p/q where both p and q are integers and q ≠ 0.
Finding The Cube Root Of 432
Finding cube roots for perfect cubes is easy, but for non-perfect cubes, the process can be a bit tricky. For non-perfect cubes, we can use Halley’s method. Let’s explore how this method helps us find the cube root of 432.
Cube Root Of 432 By Halley’s Method
Halley’s method is a step-by-step way to find the cube root of a non-perfect cube number. Here, we will find the value of ‘a’ where a3 is the non-perfect cube
∛a≅ x (x3+2a) (2x3+a) is the formula used in this method.
As 432 is a non-perfect cube number, it lies between the two perfect cube numbers. Here, ‘a’ lies between 343 (73) and 512 (83).
By applying Halley’s Method, we get
Step 1: Let the number ‘a’ = 432. Start by taking ‘x’ = 343, as 343 (∛343 = 7) is the nearest perfect cube which is closer to 432
Step 2: Apply the value of ‘a=432’ and ‘x=343’ in the formula:
∛a≅ x (x3+2a) / (2x3+a)
Step 3: The formula will be,
∛432 ≅ 343 (3433+2*432) / (2*3433+432)
Step 4: After simplifying, we get the cube root of 432 as 7.559526299.
Common Mistakes And How To Avoid Them In Finding Cube Root Of 432
Making mistakes while learning cube roots is common. Let’s look at some common mistakes kids might make and how to fix them.
Mistake 1
Incorrect calculation after applying values in the formula
Sometimes instead of using the ‘+’ symbol, kids may accidentally use the multiplication symbol ‘×’. This can lead to wrong calculations and incorrect results. Always double-check the symbols used in the formula to make sure you’re adding, not multiplying, when needed.
Cube Root Of 432 Examples
Problem 1
What is the cube root of 432?
The cube root of 432 is approximately 7.57.
Explanation
The cube root of a number is the value that, when multiplied by itself three times, equals the original number. For 432.
∛432 = 7.57
Problem 2
What is the approximate value of ∛432 in fraction form?
∛432 ≈ 27/4.
Explanation
The cube root of 432 in decimal form is approximately 7.57. To express this as a fraction:
7.57 = 757/100
Simplifying, we get a close approximation of 27/4
Thus, ∛432 ≈ 27/4 is the required fraction form.
Problem 3
Question: What’s the cube of 7.6?
The cube of 7.6 is 438.98.
Explanation
The cube of a number is found by multiplying the number by itself three times. For 7.6:
7.63 = 7.6×7.6×7.6 = 438.976
Rounding to two decimal places gives 438.98.
Thus, the cube of 7.6 is approximately 438.98.
Problem 4
Question: Is ∛432 less than 7?
No, ∛432 (7.57) is not less than 7.
Explanation
The cube root of 432 is approximately 7.57, which is greater than 7. To determine this,
∛432 = 7.57
Since 7.57 ＞7, the cube root of 432 is not less than 7.
Problem 5
What is the square of 50?
The square of 50 is 2500.
Explanation
To find the square of a number, multiply the number by itself:
502 = 50×50 = 2500
Thus, the square of 50 is 2500.
FAQs For Cube Root 432
1.How close to 7 is the cube root of 432, and how close to 8?
2.Which integer is closest to the cube root of 432?
3.Is ∛432 rational?
4.Can ∛432 be a perfect cube?
5.What is the cube root of a negative number?
6.How does learning Algebra help students in Saudi Arabia make better decisions in daily life?
7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Cube Root Of 432?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Cube Root Of 432?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
Important Glossaries For Cube Root Of 432
- Prime Factorization: It is the process of expressing a number as a product of its prime factors. In other words, it involves breaking the number down into prime numbers that multiply together to give the original number.
- Square root: The square root of a number is a value ‘y’ such that, when ‘y’ is multiplied by itself, it equals the original number. In other words, if y × y = x, then y is the square root of x.
- Rational numbers: The number which can be expressed as p/q, where p and q are integers and q≠ 0 are called Rational numbers.
- Irrational numbers: The number which cannot be expressed as p/q, where p and q are integers and q ≠ 0 are called Irrational numbers. These numbers are non-terminating, non-repeating decimal representations.
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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.
