224 LearnersLast updated on May 26th, 2025
Cube Root of 120
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 120, and its examples
What Is the Cube Root of 120?
The cube root of 120 is the value which, when multiplied by itself three times (cubed), gives the original number 120. The cube root of 120 is 4.93242414866. The cube root of 120 is expressed as ∛120 in radical form, where the “ ∛ ” sign” is called the “radical” sign. In exponential form, it is written as (120)â…“. If “m” is the cube root of 120, then, m3=120. Let us find the value of “m”.
Finding the Cubic Root of 120
We can find cube roots of 120 through a method, named as, Halley’s Method. Let us see how it finds the result.
Cube Root of 120 By Halley’s 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 ∛a≅ 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 120.
Step 1: Let a=120. Let us take x as 4, since 43=64 is the nearest perfect cube which is less than 120.
Step 2: Apply the formula. ∛120≅ 4((43+2×120) / (2(4)3+120)) = 4.9…
Hence, 4.9… is the approximate cubic root of 120.
Common Mistakes and How to Avoid Them in the Cube Root of 120
Understanding common misconceptions or mistakes can make your calculations error free. So let us see how to avoid those from happening.
Mistake 1
For ∛120, 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 120 Examples
Problem 1
The length, breadth, and height of a cuboid is 6 units, 6.5 units, and 6.8 units respectively. To find its volume, also find the measure of a side of a cube whose volume is 120 cubic units.
Volume of a cuboid = length × breadth × height = 6 × 6.5 × 6.8 cubic units = 265.2 cubic units.
Given, Volume of a cube = 120 cubic units
⇒ side × side × side = 120 cubic units
⇒ side = ∛120
⇒ side = 4.9 units
Answer: Volume of the cuboid = 265.2 cubic units
Side length of the cube = 4.9 units
Explanation
Applied the formula and concept of the volume of a cuboid and cube and solved.
Problem 2
Find ∛120 / 49.32.
(∛120) / 49.32
= 4.932 /49.32
= 0.1
Answer: 0.1
Explanation
Simplified the expression, and found out the result.
Problem 3
Multiply ∛120 × ∛216 / ∛125
∛120 × âˆ›216 × âˆ›125
= 4.93 × 6 /5
= 5.916
Answer: 5.916
Explanation
We know that the cubic root of 216 is 6 and the cubic root of 125 is 5, hence multiplying ∛216, ∛125 and ∛120.
Problem 4
Find ∛(120+(-20)+(-36)).
∛(120-20-36)
= ∛64
=4
Answer: 4
Explanation
Simplified the expression, and found out the cubic root of the result.
FAQs on 120 Cube Root
1.Is 121 a cube root?
2.Is 120 a perfect square ?
3.Which perfect cube number is closest to 120?
4.What is an imperfect cube?
5.How do I calculate √120?
6.How does learning Algebra help students in Thailand make better decisions in daily life?
7.How can cultural or local activities in Thailand support learning Algebra topics such as Cube Root of 120?
8.How do technology and digital tools in Thailand support learning Algebra and Cube Root of 120?
9.Does learning Algebra support future career opportunities for students in Thailand?
Important Glossaries for Cube Root of 120
- 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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