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

Learn how to find the Cube Root of 120 using methods like Halley’s Method, and more. Perfect for Math lovers!

Cube Root of 120 | How to Find 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. &nbsp;The cube root of 120 is expressed as ∛120 in radical form, where the &ldquo; ∛ &rdquo; &nbsp;sign&rdquo; is called the &ldquo;radical&rdquo; sign. In exponential form, it is written as (120)⅓. If &ldquo;m&rdquo; is the cube root of 120, then, m3=120. Let us find the value of &ldquo;m&rdquo;. 
&nbsp;

We can find cube roots of 120 through a method, named as, Halley&rsquo;s Method. Let us see how it finds the result. 
&nbsp;

Now, what is Halley&rsquo;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 &ldquo;x&rdquo;.

 
Formula is ∛a&cong; x((x3+2a) / (2x3+a)), where

&nbsp;

 
a=given number whose cube root you are going to find

 
x=integer guess for the cubic root

 
Let us apply Halley&rsquo;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. &nbsp;∛120&cong; 4((43+2&times;120) / (2(4)3+120)) = 4.9&hellip;

 
Hence, 4.9&hellip; is the approximate cubic root of 120. 
&nbsp;

Understanding common misconceptions or mistakes can make your calculations error free. So let us see how to avoid those from happening. 
&nbsp;

Common Mistakes and How to Avoid Them in the Cube Root of 120

For ∛120, students can make error in the important part of prime factorization. 
&nbsp;

&nbsp;Applying exponent rules incorrectly when finding cube roots. 
&nbsp;

&nbsp;For large non-perfect cubes, students frequently estimate wrongly and leave it with a wrong result.&nbsp; 
&nbsp;

Students typically rely on memorizing rather than understanding concepts of cube root.&nbsp; 
&nbsp;

&nbsp;Misapply the cube root property like when asked to solve ∛(120)3, students might do as ∛(120&times;3) 
&nbsp;

<ul>
	<li>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.&nbsp;</li>
	<li>&nbsp;</li>
</ul>

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

&nbsp;

<ul>
	<li>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.</li>
</ul>

&nbsp;

<ul>
	<li>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.</li>
</ul>

&nbsp;

<ul>
	<li>Polynomial - It is an algebraic expression made up of variables like &ldquo;x&rdquo; and constants, combined using addition, subtraction, multiplication, or division, where the variables are raised to whole number exponents.</li>
</ul>

&nbsp;

<ul>
	<li>Approximation - Finding out a value which is near to the correct answer, but not perfectly correct.</li>
</ul>

&nbsp;

<ul>
	<li>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.&nbsp; 
	&nbsp;</li>
</ul>

Cube Root of 120

What Is the Cube Root of 120?

Finding the Cubic Root of 120

Cube Root of 120 By Halley’s Method

Explore More algebra