218 LearnersLast updated on May 26th, 2025
Cube Root of 48
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
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.
Mistake 1
For ∛48, 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).
Mistake 2
Students forget the concept of cube roots often, by not understanding the definition.
This happens because of uncleared understanding of cube roots and the methods to find it.
Mistake 3
For large non-perfect cubes, students frequently estimate wrongly and leave it with a wrong result.
Keep the methods of finding cube roots in front whenever attempting large non-perfect cubes.
Mistake 4
Students typically rely on memorizing rather than understanding concepts of cube root.
Memorizing is not the solution when it comes to complex problems. So understanding the methods of finding cube roots is advisable.
Mistake 5
Misapply the cube root property like when asked to solve ∛(48)3, students might do as ∛(48×3)
Clear the concepts again and again if they don’t understand, where to do what. ∛(48)3≠∛(48×3). ∛(48)3= 48
Cube Root of 48 Examples
Problem 1
Find ((∛96/ ∛48) × (∛96/ ∛48) × (∛96/ ∛48))
(∛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.
Problem 2
If y = ∛48, find y³/ y⁶
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.
Problem 3
Multiply ∛48 × ∛64 × ∛125
∛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.
Problem 4
What is ∛(100)⁶+ ∛(48)⁶ ?
∛(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.
Problem 5
Find ∛(48+(-8)+(-13)).
∛(48-8-13)
= ∛27
=3
Answer: 3
Explanation
Simplified the expression, and found out the cubic root of the result.
FAQs on 48 Cube Root
1.How to solve √48 ?
2.Is 48 a perfect square ?
3.How to solve 3√4913 ?
4.What is the square root of 48 in the simplest form?
5.How do I calculate √47?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Cube Root of 48?
8.How do technology and digital tools in Australia support learning Algebra and Cube Root of 48?
9.Does learning Algebra support future career opportunities for students in Australia?
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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About BrightChamps in Australia
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.
