Last updated on May 26th, 2025
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.
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”.
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.
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.
here's some common mistakes with their solutions given below:
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
We solved and simplified the exponent part first using the fact that, β32=(32)β
and β16=(16)β
, then solved.
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
(β16)3=(161/3)3=16, and β16)6=(161/3)6=(16)2. Using this, we found the value of y3/y6.
Multiply β16 Γ β64
β16×β64
= 2.519×4
= 10.076
Answer: 10.076
We know that the cubic root of 64 is 4, hence multiplying β64 with β16.
What is β(16βΆ) ?
β(166)
= ((16)6))1/3
=( 16)2
= 256
Answer: 256
We solved and simplified the exponent part first using the fact that, β16=(16)β
, then solved.
Find β(16+(-8)).
β(16-8)
= β8
= 2
Answer: 2
Simplified the expression, and found out the cube root of the result.
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.
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