485 LearnersLast updated on May 26th, 2025
Cube Root of 16
The cube root of 16 is the value that, when multiplied by itself three times (cubed), gives the original number 16. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, density and mass, field of engineering etc.
What Is the Cube Root of 16?
The cube root of 16 is 2.51984209979. The cube root of 16 is expressed as β16 in radical form, where the “ β ” sign is called the “radical” sign. In exponential form, it is written as (16)β . If “m” is the cube root of 16, then, m3=16. Let us find the value of “m”.
Finding the Cube Root of 16
The cube root of 16 is expressed as 2β2 as its simplest radical form,
since 16 = 2×2×2×2
β16 = β(2×2×2×2)
Group together three same factors at a time and put the remaining factor under the β .
β16= 2β2
We can find cube root of 16 through a method, named as, Halley’s Method. Let us see how it finds the result.
Cube Root of 16 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 16.
Step 1: Let a=16. Let us take x as 2, since, 23=8 is the nearest perfect cube which is less than 16.
Step 2: Apply the formula. β16≅ 2((23+2×16) / (2(2)3+16))= 2.5
Hence, 2.5 is the approximate cubic root of 16.
Common Mistakes and How to Avoid Them in the Cube Root of 16
here's some common mistakes with their solutions given below:
Mistake 1
Students might make errors during factorization. For β16, students can make error in the crucial part and write β16= 23 .
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 often 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 often rely on memorising rather than understanding concepts of cube root.
Memorising 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(16)3, students might do as β(16×3)
Clear the concepts again and again if they don’t understand where to do what. β(16)3≠β(16×3).
β(16)3= 16
Cube Root of 16 Examples
Problem 1
Find (β32/ β16) Γ (β32/ β16) Γ (β32/ β16)
(β32/ β16) × (β32/ β16) × (β32/ β16)
= (β32× β32× β32) / (β16× β16× β16)
= ((32)β
)3/ ((16)β
)3
= 32/16
= 2
Answer: 2
Explanation
We solved and simplified the exponent part first using the fact that, β32=(32)β
and β16=(16)β
, then solved.
Problem 2
If y = β16, find y^3/ y^6
y=β16
⇒ y3/y6= (β16)3 / (β16)6
⇒ y3/y6
= 16/ (16)2
= 1/16
Answer: 1/16
Explanation
(β16)3=(161/3)3=16, and β16)6=(161/3)6=(16)2. Using this, we found the value of y3/y6.
Problem 3
Multiply β16 Γ β64
β16×β64
= 2.519×4
= 10.076
Answer: 10.076
Explanation
We know that the cubic root of 64 is 4, hence multiplying β64 with β16.
Problem 4
What is β(16βΆ) ?
β(166)
= ((16)6))1/3
=( 16)2
= 256
Answer: 256
Explanation
We solved and simplified the exponent part first using the fact that, β16=(16)β
, then solved.
Problem 5
Find β(16+(-8)).
β(16-8)
= β8
= 2
Answer: 2
Explanation
Simplified the expression, and found out the cube root of the result.
FAQs on 16 Cubic Root
1.What perfect cube goes into 16?
2.How to solve 4β16 ?
3.What is the cube root of 8?
4.Is β16 a complex number?
5.What is the 5th root of 32?
Important Glossaries for Cube Root of 16
- 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.
- 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.
