356 LearnersLast updated on May 26th, 2025
Cube Root of 192
The cube root of 192 is the value that, when multiplied by itself three times (cubed), gives the original number 192. Do you know? Cube roots apply to our real life also, like that for measuring volume and scaling, density and mass calculation, etc.
What Is the Cubic Root of 192?
The cube root of 192 is 5.76899828123. The cube root of 192 is expressed as ∛192 in radical form, where the “∛" sign is called the “radical” sign. In exponential form, it is written as (192)â…“. If “m” is the cube root of 192, then, m3=192. Let us find the value of “m”.
Finding the Cubic Root of 192
The cube root of 192 is expressed as 4∛3 as its simplest radical form, since
192 = 2×2×2×2×2×2×3
∛192 = ∛(2×2×2×2×2×2×3)
Group together three same factors at a time and put the remaining factor under the ∛ .
∛192= 4∛3
We can find cube root of 192 through a method, named as, Halley’s Method. Let us see how it finds the result.
Cubic Root of 192 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 192.
Step 1: Let a=192. Let us take x as 5, since, 125 is the nearest perfect cube which is less than 192.
Step 2: Apply the formula. ∛192≅ 5((53+2×192) / (2(5)3+192))=5.757
Hence, 5.757 is the approximate cubic root of 192.
Common Mistakes and How to Avoid Them in the Cubic Root of 192
some common mistakes with their solutions are given below:
Mistake 1
Children get confused of the concept of cube root with that of square root.
The Cube root of 192 is ∛192, and the square root of 192 is √192. Understand the definition of Cube roots and square
root.
Mistake 2
Misidentifying prime numbers with composite numbers while performing prime factorization to find cube roots.
While prime factorization, make sure you know which numbers are prime and which are not.Identify the prime numbers.
Mistake 3
Applying exponent rules incorrectly when finding cube roots.
∛192 is not same as 1923. ∛192 = 5.768… and 1923=7077888.
Mistake 4
Students often calculate mentally the value of cube roots.
Students can use Prime factorization method or Halley’s method to find out the approximate value for cube roots.
Mistake 5
Not checking for perfect cubes, like that of 125, before using calculators for approximation.
Try to remember which are the perfect cubes, at least from 1 to 200.
Cubic Root of 192 Examples
Problem 1
Find ∛192/ ∛8
∛192/ ∛8
= 5.768 / 2
= 2.884
Answer: 2.884
Explanation
We know that the cubic root of 8 is 2, hence dividing ∛192 by 2.
Problem 2
The Volume of a cube is 192 cubic centimeters, find the length of one side of the cube.
We know that, (side of a cube)3=Volume of a cube
⇒side of the cube = ∛(Volume of the cube)
⇒side of the cube = ∛192
⇒ side of the cube = 5.768 cm
Answer: 5.768 cm
Explanation
We applied the formula for finding the volume of a cube, and inverted it to find the measure of one side of the cube.
Problem 3
Subtract ∛192 - ∛125
∛192-∛125
= 5.768–5
= 0.768.
Answer: 0.768
Explanation
We know that the cubic root of 8 is 2, hence subtracting ∛125 from ∛192.
Problem 4
What is ∛(192²) ?
∛(1922)
= ∛36864
= 33.281…
Answer: 33.281…
Explanation
We first found the square value of 192, which is 36864, and then found out the cube root of 36864.
Problem 5
Find ∛(192+24).
∛(192+24)
= ∛216
=6
Answer: 6
Explanation
Simplified the expression, and found out the cubic root of the result.
FAQs on 192 Cubic Root
1.What is the simplified cube root of 192?
2.What are the factors of 192?
3.What is the cube root of minus 192 by 81?
4.What is the factorization of 192?
5.What is the smallest number by which 192 can be divided to get a perfect cube?
Important Glossaries for Cubic Root of 192
- Integers - Integers can be a positive natural number, negative of a positive number, or zero. We can perform all the arithmetic operations on integers. The examples of integers are, 1, 2, 5,8, -8, -12, etc.
- 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 value “y” such that when “y” is multiplied by itself → y × y, the result is the original number.
- 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.
- 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.
