Last updated on May 26th, 2025
We will learn the cube root concept to use it on other mathematical topics like algebra, mensuration, geometry, trigonometry, etc. So, it is as important as learning square roots. Let us now see how we can obtain the cube root value of 50, and its examples.
The cube root of 50 is the value which, when multiplied by itself three times (cubed), gives the original number 50. The cube root of 50 is 3.68403149864. The cube root of, 50 is expressed as β50 in radical form, where the “ β ” sign” is called the “radical” sign. In exponential form, it is written as (50)β
. If “m” is the cube root of 50, then, m3=50. Let us find the value of “m”.
We can find cube roots of 50 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, 50.
Step 1: Let a=50. Let us take x as 3, since 33=27 is the nearest perfect cube which is less than 50.
Step 2: Apply the formula. β50≅ 3((33+2×50) / (2(3)3+50)) = 3.66…
Hence, 3.66… is the approximate cubic root of 50.
Understanding common misconceptions or mistakes can make your calculations error free. So let us see how to avoid those from happening.
Find ((β150/ β50) Γ (β150/ β50) Γ (β150/ β50))
(β150/ β50) × (β150/ β50) × (β150/ β50)
= (β150× β150× β150) / (β50× β50× β50)
=((150)β
)3/ ((50)β
)3
=150/50
=3
Answer: 3
We solved and simplified the exponent part first using the fact that, β150=(150)β
and β50=(50)β
, then solved.
If y = β50, find (yΒ³/ yβΆ)Γ(yΒ²/yβ΄)ΓyΒ³
: y=β50
⇒ (y3/ y6)×(y2/y4)
= ((β50)3 / (β50)6)×((β50)2 / (β50)4)× (β50)3
⇒ (y3/ y6)×(y2/y4)= (50/ (50)2) × (502/3-4/3)×(50)= 1/(50)2/3
Answer:1/(50)2/3
(β50)3=(501/3)3=50, β(50)6=(501/3)6=(50)2, (β50)2=(501/3)2=502/3, and (β50)4=(501/3)4=(50)4/3 Using this, we found the value of (y3/ y6)×(y2/y4)×y3.
Multiply β50 Γ β1000 Γ β125
β50 × β1000 × β125
= 3.66 × 10 ×5
= 183
Answer: 183
We know that the cubic root of 1000 is 10 and the cubic root of 125 is 5, hence multiplying β125, β1000 and β50.
What is β(10)βΆ + β(50)βΆ?
β(106)+ β(50)6
= ((10)6))1/3 +((50)6)1/3
=(10)2 + (50)2
= 100 + 2500
Answer: 2600
We solved and simplified the exponent part first using the fact that, β10=(10)β
and β50=(50)β
, then solved.
2) The cube root of a negative number is also negative.
3) If the cube root of a number is a whole number, then that original number is said to be perfect cube
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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