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Cube Root of 100

The value of the cube root of 100 rounded to 6 decimal places is 4.641589. It is the real solution of the equation x³ = 100. The cube root of 100 is expressed as ∛100 in the radical form and as (100)^⅓ or (100)^0.33 in the exponent form. The prime factorization of 100 is 2 × 2 × 5 × 5, hence, the cube root of 100 in its lowest radical form is expressed as ∛100.

Cube root of 100: 4.641588834
Cube root of 100 in Exponential Form: (100)^⅓
Cube root of 100 in Radical Form: ∛100

1.	What is the Cube Root of 100?
2.	How to Calculate the Cube Root of 100?
3.	Is the Cube Root of 100 Irrational?
4.	FAQs on Cube Root of 100

What is the Cube Root of 100?

The cube root of 100 is the number which when multiplied by itself three times gives the product as 100. Since 100 can be expressed as 2 × 2 × 5 × 5. Therefore, the cube root of 100 = ∛(2 × 2 × 5 × 5) = 4.6416.

☛ Check: Cube Root Calculator

How to Calculate the Value of the Cube Root of 100?

Cube Root of 100 by Halley's Method

Its formula is ∛a ≈ x ((x³ + 2a)/(2x³ + a))
where,
a = number whose cube root is being calculated
x = integer guess of its cube root.

Here a = 100
Let us assume x as 4
[∵ 4³ = 64 and 64 is the nearest perfect cube that is less than 100]
⇒ x = 4
Therefore,
∛100 = 4 (4³ + 2 × 100)/(2 × 4³ + 100)) = 4.63
⇒ ∛100 ≈ 4.63
Therefore, the cube root of 100 is 4.63 approximately.

Is the Cube Root of 100 Irrational?

Yes, because ∛100 = ∛(2 × 2 × 5 × 5) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 100 is an irrational number.

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Cube Root of 100 Solved Examples

Example 1: What is the value of ∛100 + ∛(-100)?

Solution:

The cube root of -100 is equal to the negative of the cube root of 100.
i.e. ∛-100 = -∛100

Therefore, ∛100 + ∛(-100) = ∛100 - ∛100 = 0
Example 2: Given the volume of a cube is 100 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 100 in³ = a³
⇒ a³ = 100
Cube rooting on both sides,
⇒ a = ∛100 in
Since the cube root of 100 is 4.64, therefore, the length of the side of the cube is 4.64 in.
Example 3: The volume of a spherical ball is 100π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 100π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 100
⇒ R = ∛(3/4 × 100) = ∛(3/4) × ∛100 = 0.90856 × 4.64159 (∵ ∛(3/4) = 0.90856 and ∛100 = 4.64159)
⇒ R = 4.21716 in³

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FAQs on Cube Root of 100

What is the Value of the Cube Root of 100?

We can express 100 as 2 × 2 × 5 × 5 i.e. ∛100 = ∛(2 × 2 × 5 × 5) = 4.64159. Therefore, the value of the cube root of 100 is 4.64159.

What is the Cube Root of -100?

The cube root of -100 is equal to the negative of the cube root of 100. Therefore, ∛-100 = -(∛100) = -(4.642) = -4.642.

If the Cube Root of 100 is 4.64, Find the Value of ∛0.1.

Let us represent ∛0.1 in p/q form i.e. ∛(100/1000) = 4.64/10 = 0.46. Hence, the value of ∛0.1 = 0.46.

Is 100 a Perfect Cube?

The number 100 on prime factorization gives 2 × 2 × 5 × 5. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 100 is irrational, hence 100 is not a perfect cube.

How to Simplify the Cube Root of 100/343?

We know that the cube root of 100 is 4.64159 and the cube root of 343 is 7. Therefore, ∛(100/343) = (∛100)/(∛343) = 4.642/7 = 0.6631.

What is the Cube of the Cube Root of 100?

The cube of the cube root of 100 is the number 100 itself i.e. (∛100)³ = (100^1/3)³ = 100.