Last updated on May 26th, 2025
The cube root of 100 is the value that, when multiplied by itself three times (cubed), gives the original number 100. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, creating digital art, field of engineering, making financial decisions etc.
The cube root of 100 is 4.64158883361. The cube root of 100 is expressed as ∛100 in radical form, where the “ ∛ ” sign is called the “radical” sign. In exponential form, it is written as (100)⅓. If “m” is the cube root of 100, then, m3=100. Let us find the value of “m”.
The cube root of 100 is expressed as ∛100 as its simplest radical form,
since 100 = 2×2×5×5
∛100 = ∛(2×2×5×5)
Group together three same factors at a time and put the remaining factor under the ∛ .
∛100= ∛100
We can find cube root of 100 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 ∛a≅ 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 100.
Step 1: Let a=100. Let us take x as 4, since, 43=64 is the nearest perfect cube which is less than 100.
Step 2: Apply the formula. ∛100≅ 4((43+2×100) / (2(4)3+100))= 4.63…
Hence, 4.63… is the approximate cubic root of 100.
Here are some common mistakes with their solutions given :
Find (∛200/ ∛100) × (∛200/ ∛100) × (∛200/ ∛100)
(∛200/ ∛100) × (∛200/ ∛100) × (∛200/ ∛100)
= (∛200× ∛200× ∛200) / (∛100× ∛100× ∛100)
=((200)⅓)3/ ((100)⅓)3
=200/100
=2
Answer: 2
We solved and simplified the exponent part first using the fact that, ∛200=(100)⅓ and ∛100=(100)⅓, then solved.
If y = ∛100, find y³/ y⁶
y=∛100
⇒ y3/y6= (∛100)3 / (∛100)6
⇒ y3/y6
= 100/ (100)2
= 1/100
Answer: 1/100
(∛100)3=(1001/3)3=100, and ∛100)6=(1001/3)6=(16)2. Using this, we found the value of y3/y6.
Multiply ∛100 × ∛125
∛100×∛125
= 4.641×5
=23.205
Answer: 23.205
We know that the cubic root of 125 is 5, hence multiplying ∛125 with ∛100.
What is ∛(100⁶) ?
∛(1006)
= ((100)6))1/3
=( 100)2
= 10000
Answer: 10000
We solved and simplified the exponent part first using the fact that, ∛100=(100)⅓, then solved.
Find ∛(100+(-36)).
∛(100-36)
= ∛64
=4
Answer: 4
Simplified the expression, and found out the cubic 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.
: He loves to play the quiz with kids through algebra to make kids love it.