218 LearnersLast updated on May 26th, 2025
Cube Root of 48
In math, the cube root of 48 is expressed as β48 in radical form, where the β β β signβ is called the βradicalβ 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)β
. 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 Halleyβs 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 βa≅ 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. β48≅ 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 β48, 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 β(48)3, students might do as β(48×3)
Clear the concepts again and again if they don’t understand, where to do what. β(48)3≠β(48×3). β(48)3= 48
Cube Root of 48 Examples
Problem 1
Find ((β96/ β48) Γ (β96/ β48) Γ (β96/ β48))
(β96/ β48) × (β96/ β48) × (β96/ β48)
= (β96× β96× β96) / (β48× β48× β48)
=((96)β
)3/ ((48)β
)3
=96/48
=2
Answer: 2
Explanation
We solved and simplified the exponent part first using the fact that, β96=(96)β
and β48=(48)β
, then solved.
Problem 2
If y = β48, find yΒ³/ yβΆ
y=β48
⇒ y3/y6
= (β48)3 / (β48)6
⇒ y3/y6= 48/ (49)2= 1/48
Answer: 1/48
Explanation
(β48)3=(481/3)3=48, and β(48)6=(481/3)6=(48)2. Using this, we found the value of y3/y6.
Problem 3
Multiply β48 Γ β64 Γ β125
β48 × β64 × β125
= 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 β125, β64 and β48.
Problem 4
What is β(100)βΆ+ β(48)βΆ ?
β(1006)+ β(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, β100=(100)β
and β48=(48)β
, then solved.
Problem 5
Find β(48+(-8)+(-13)).
β(48-8-13)
= β27
=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 β48 ?
2.Is 48 a perfect square ?
3.How to solve 3β4913 ?
4.What is the square root of 48 in the simplest form?
5.How do I calculate β47?
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.
