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 66, and its examples.
The cube root of 66 is the value which, when multiplied by itself three times (cubed), gives the original number 66. The cube root of 66 is 4.04124002062. The cube root of, 66 is expressed as β66 in radical form, where the “ β ” sign” is called the “radical” sign. In exponential form, it is written as (66)β
. If “m” is the cube root of 66, then, m3=66. Let us find the value of “m”.
We can find cube roots of 66 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, 66.
Step 1: Let a=66. Let us take x as 4, since 43=64 is the nearest perfect cube which is less than 64.
Step 2: Apply the formula. β64≅ 4((43+2×66) / (2(4)3+66)) = 4.04…
Hence, 4.04… is the approximate cubic root of 66.
Understanding common misconceptions or mistakes can make your calculations error free. So let us see how to avoid those from happening.
Find (β22/ β66) Γ (β22/ β66) Γ (β22/ β66)
(β22/ β66) × (β22/ β66) × (β22/ β66)
= (β22× β22× β22) / (β66× β66× β66)
=((22)β
)3/ ((66)β
)3
=22/66
=1/3
Answer: 1/3
We solved and simplified the exponent part first using the fact that, β22=(22)β and β66=(66)β , then solved.
If y = β66, find yΒ³/ yβΉ
y=β66
⇒ y3/y9= (β66)3 / (β66)9
⇒ y3/y9= 66/ (66)3= 1/(66)2
Answer: 1/(66)2
(β66)3=(661/3)3=66, and β(66)9=(661/3)9=(66)3. Using this, we found the value of y3/y9.
Multiply β66 Γ β1000
β66×β1000
= 4.04×10
=40.4
Answer: 40.4
We know that the cubic root of 1000 is 10, hence multiplying β1000 with β66.
Solve the equation: (x)Β³/Β²=66
(x)3/2=66
⇒ (x)1/2=(66)1/3
⇒ (x)1/2 = 4.04
⇒ (x) = (4.04)2
⇒ x= 16.3216
Answer: 16.3216
Simplified the equation applying the cube root features and found the answer.
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.
: He loves to play the quiz with kids through algebra to make kids love it.