Cube Root of 120
2026-02-28 01:34 Diff
https://brightchamps.com/en-us/math/algebra/cube-root-of-120

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Last updated on August 5, 2025

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)⅓. 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.
 

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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.
 

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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.

Okay, lets begin

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.
 

Well explained 👍

Problem 2

Find ∛120 / 49.32.

Okay, lets begin

 (∛120) / 49.32

= 4.932 /49.32

= 0.1


Answer: 0.1
 

Explanation

Simplified the expression, and found out the result. 
 

Well explained 👍

Problem 3

Multiply ∛120 × ∛216 / ∛125

Okay, lets begin

∛120 ×  ∛216  × ∛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.
 

Well explained 👍

Problem 4

Find ∛(120+(-20)+(-36)).

Okay, lets begin

 ∛(120-20-36)

= ∛64

=4


Answer: 4
 

Explanation

Simplified the expression, and found out the cubic root of the result. 
 

Well explained 👍

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?

125, which is a perfect cube firstly, and the cube of 5, i.e., 5×5×5=125 is the nearest perfect cube to 120.
 

4.What is an imperfect cube?

An imperfect cubes are the numbers which are not the product of a whole number multiplied by itself thrice, rather, they are the product of irrational numbers.
 

5.How do I calculate √120?

√120 can be calculated through methods like Long Division, Approximation etc. The value of √120 is 10.954…
 

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. 
     

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.