239 LearnersLast updated on May 26th, 2025
Cube Root of 384
We will learn the cube root concept to use it on other mathematical topics like algebra, mensuration, geometry, trigonometry, etc. So, it is as important as learning square roots. Let us now see how we can obtain the cube root value of 384, and its examples.
What Is the Cube Root of 384?
The cube root of 384 is the value which, when multiplied by itself three times (cubed), gives the original number 384.
The cube root of 384 is 7.26848237133. The cube root of 384 is expressed as β384 in radical form, where the “ β ” sign” is called the “radical” sign. In exponential form, it is written as (384)β . If “m” is the cube root of 384, then, m3=384. Let us find the value of “m”.
Finding the Cubic Root of 384
We can find cube roots of 384 through a method, named as, Halley’s Method. Let us see how it finds the result.
Cubic Root of 384 By Halleyβs Method
Now, what is Halley’s Method? It is an iterative method for finding cube roots of a given number N, such that, x3=N, where this method approximates the value of “x”.
Formula is βa≅ x((x3+2a) / (2x3+a)), where
a=given number whose cube root you are going to find
x=integer guess for the cubic root
Let us apply Halley’s method on the given number 384.
Step 1: Let a=384. Let us take x as 7, since 73=343 is the nearest perfect cube which is less than 384.
Step 2: Apply the formula. β384≅ 7((73+2×384) / (2(7)3+384)) = 7.27…
Hence, 7.27… is the approximate cubic root of 384.
Common Mistakes and How to Avoid Them in the Cube Root of 384
Understanding common misconceptions or mistakes can make your calculations error free. So let us see how to avoid those from happening.
Mistake 1
For β384, students can make error in the important part of prime factorization.
Prime Factorization is a crucial part in determining cube roots and square roots. So, use the exact prime factors and group (or pair).
Cube Root of 384 Examples
Problem 1
Find ((β768/ β384) Γ (β768/ β384) Γ (β768/ β384))
(β768/ β384) × (β768/ β384) × (β768/ β384)
= (β768× β768× β768) / (β384× β384× β384)
=((768)β
)3/ ((384)β
)3
=768/384
=2
Answer: 2
Explanation
We solved and simplified the exponent part first using the fact that, β678=(96)β
and β384=(384)β
, then solved.
Problem 2
If y = β384, find yΒ²/ yβΆ
y=β384
⇒ y3/y6= (β384)3 / (β384)6
⇒ y3/y6= 384/ (384)2= 1/384
Answer: 1/384
Explanation
(β384)3
=(3841/3)3
=384, and β(384)6=(3841/3)6=(384)2.
Using this, we found the value of y3/y6
Problem 3
Multiply β384 Γ β64 Γ β125
β384 × β64 × β125= 7.27 × 4 ×5= 145.4
Answer: 145.4
Explanation
We know that the cubic root of 64 is 4 and the cubic root of 125 is 5, hence multiplying β125, β64 and β384.
Problem 4
What is β(100)βΆ + β(384)βΆ?
β(1006)+ β(384)6
= ((100)6))1/3 +((384)6)1/3
=(100)2 + (384)2
= 10000 + 147456
Answer: 147456
Explanation
We solved and simplified the exponent part first using the fact that, β100=(100)β
and β384=(384)β
, then solved.
Problem 5
Find β(384+(-20)+(-21)).
β(384-20-21)
= β343
=7
Answer: 7
Explanation
Simplified the expression, and found out the cubic root of the result.
FAQs on 384 Cube Root
1.How to solve β384 ?
2.Is 384 a perfect square ?
3.How to find the cube root of 343?
4.What is the square root of 384 in the simplest form?
5.How do I calculate β385?
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 384?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Cube Root of 384?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
Important Glossaries for Cube Root of 384
- Cube root properties - The features when cube root is applied to any number. Those are: 1) The cube root of all odd numbers is an odd number. The same applies for even numbers also, that is, the cube of any even number is even.
2) The cube root of a negative number is also negative.
3) If the cube root of a number is a whole number, then that original number is said to be perfect cube
- Irrational Numbers - Numbers which cannot be expressed as m/n form, where m and n are integers and n not equal to 0, are called Irrational numbers.
- Square root -The square root of a number is a number which when multiplied by itself produces the original number, whose square root is to be found out.
- Polynomial - It is an algebraic expression made up of variables like “x” and constants, combined using addition, subtraction, multiplication, or division, where the variables are raised to whole number exponents.
- Approximation - Finding out a value which is near to the correct answer, but not perfectly correct.
- Iterative method - This method is a mathematical process which uses an initial value to generate a further sequence of solutions for a problem, step-by-step.
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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
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