Last updated on May 26th, 2025
The cube root of 3 is the value which, when multiplied by itself three times (cubed), gives the original number 3. Do you know? Cube roots are there in our real life too, like that for measuring dimensions, density and mass, field of engineering etc.
The cube root of 3 is 1.44224957031. The cube root of 3 is expressed as β3 in radical form, where the ββ" the sign is called the βradicalβ sign. In exponential form, it is written as (3)β
. If βmβ is the cube root of 3, then, m3=3. Let us find the value of βmβ.
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The cube root of 3 is expressed as β3 as its simplest radical form. We can find cube root of 3 through a method, named as, Halleyβs Method. Let us see how it finds the result.
Now, what is Halleyβs 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 βxβ.
Formula is βaβ
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 Halleyβs method on the given number 3.
Step 1: Let a=3. Let us take x as 1, since, 13=1 is the nearest perfect cube which is less than 3.
Step 2: Apply the formula. β3β
1((13+2Γ3) / (2(1)3+3))= 1.4
Hence, 1.4 is the approximate cubic root of 3.
Understanding common misconceptions or mistakes can make your calculations error free. So let us see how to avoid those from happening.
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Find ((β3/ β6) Γ (β3/ β6) Γ (β3/ β6)) + (((β3/ β6) Γ (β3/ β6) Γ (β3/ β6))
((β3/ β6) Γ (β3/ β6) Γ (β3/ β6)) +((β3/ β6) Γ (β3/ β6) Γ (β3/ β6))
= ((β3Γ β3Γ β3) / (β6Γ β6Γ β6)) + ((β3Γ β3Γ β3) / (β6Γ β6Γ β6))
=((3)β
)3/ ((6)β
)3 + ((3)β
)3/ ((6)β
)
=3/6 + 3/6
= 1/2 + 1/2
=1
Answer: 1
We solved and simplified the exponent part first using the fact that, β3=(3)β
and β6=(6)β
, then solved.
If y = β3, find yΒ³.
y=β3
β y3= (β3)3
β y3= 3
Answer: 3
(β3)3=(31/3)3=3. Using this, we found the value of y3.
Subtract β3 + β27 + β9 + β27
β3 + β27 + β9 + β27
= 1.442 + 3 + 3 + 5.196
= 12.638
Answer: 12.638
We know that the cubic root of 27 is 3, the square root of 9 is Β±3, and the square root of 27 is Β±5.196 hence applying these solved the problem
What is β(3βΆ) + β(3βΉ) ?
β(36) + β(39)
= ((3)6))1/3 + ((3)9)1/3
=(3)2 + (3)3
= 9 + 27
= 36
Answer: 36
We solved and simplified the exponent part first using the fact that, β3=(3)β
, then solved.
Find β(3+5)).
Solution:
β(3+5)
= β8
= 2
Answer: 2
Simplified the expression, and found out the cubic root of the result.
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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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