Cube Root of 48
2026-02-28 23:37 Diff
https://brightchamps.com/en-us/math/algebra/cube-root-of-48

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Last updated on August 5, 2025

In math, the cube root of 48 is expressed as ∛48 in radical form, where the “ ∛ ” sign” is called the “radical” sign. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, creating digital art, field of engineering, making financial decisions etc.

What Is the Cube Root of 48?

The cube root of 48 is the value which, when multiplied by itself three times (cubed), gives the original number 48. The cube root of 48 is 3.63424118566.  In exponential form, it is written as (48)⅓. If “m” is the cube root of 48, then, m3=48. Let us find the value of “m”.
 

Finding the Cubic Root of 48

We can find cube root of 48 through a method, named as, Halley’s Method. Let us see how it finds the result.
 

Cubic Root of 48 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 48.


Step 1: Let a=48. Let us take x as 3, since, 33=27 is the nearest perfect cube which is less than 48.


Step 2: Apply the formula.  ∛48≅ 3((33+2×48) / (2(3)3+48))= 3.62…


Hence, 3.62… is the approximate cubic root of 48
 

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Common Mistakes and How to Avoid Them in the Cube Root of 48

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

Find ((∛96/ ∛48) × (∛96/ ∛48) × (∛96/ ∛48))

Okay, lets begin

 (∛96/ ∛48) × (∛96/ ∛48) × (∛96/ ∛48)


= (∛96× ∛96× ∛96) / (∛48× ∛48× ∛48)


=((96)⅓)3/ ((48)⅓)3


=96/48


=2


Answer: 2
 

Explanation

 We solved and simplified the exponent part first using the fact that, ∛96=(96)⅓ and ∛48=(48)⅓ , then solved.
 

Well explained 👍

Problem 2

If y = ∛48, find y³/ y⁶

Okay, lets begin

 y=∛48


⇒ y3/y6

= (∛48)3 / (∛48)6


⇒ y3/y6= 48/ (49)2= 1/48


Answer: 1/48
 

Explanation

 (∛48)3=(481/3)3=48, and ∛(48)6=(481/3)6=(48)2. Using this, we found the value of y3/y6.
 

Well explained 👍

Problem 3

Multiply ∛48 × ∛64 × ∛125

Okay, lets begin

∛48 ×  ∛64  × ∛125

= 3.634 × 4 ×5

= 72.68


Answer:  72.68
 

Explanation

We know that the cubic root of 64 is 4 and the cubic root of 125 is 5, hence multiplying  ∛125, ∛64 and ∛48.
 

Well explained 👍

Problem 4

What is ∛(100)⁶+ ∛(48)⁶ ?

Okay, lets begin

 ∛(1006)+ ∛(48)6  

= ((100)6))1/3 +((48)6)1/3

=(100)2 + (48)2

= 10000 + 2304


Answer: 12304
 

Explanation

We solved and simplified the exponent part first using the fact that, ∛100=(100)⅓ and ∛48=(48)⅓ , then solved.
 

Well explained 👍

Problem 5

Find ∛(48+(-8)+(-13)).

Okay, lets begin

∛(48-8-13)

= ∛27

=3
Answer: 3
 

Explanation

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

Well explained 👍

FAQs on 48 Cube Root

1.How to solve √48 ?

48 = 2× 2× 2× 2× 3


√48 = √(2× 2× 2× 2× 3)

=4√3
 

2.Is 48 a perfect square ?

3.How to solve 3√4913 ?

 3√4913

= 3 × √(17×17×17)

= 3× 17

= 51.
 

4.What is the square root of 48 in the simplest form?

5.How do I calculate √47?

√47 can be calculated through methods like Long Division, Approximation etc. The value of √47 is 6.855…
 

Important Glossaries for Cube Root of 48

  • Irrational Numbers - All numbers cannot be expressed as p/q, where p and q are integers and q not equal to 0. Those numbers are called Irrational numbers.
  • Whole numbers - The whole numbers are part of the number system, which includes all the positive integers from 0 to infinity. 
  • 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 taken 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 nearly correct, but not perfectly correct.
  • Iterative method - This method is a mathematical process which uses an initial value to generate further and step-by-step sequence of solutions for a problem.

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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.