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Cube Root of 75

The value of the cube root of 75 rounded to 6 decimal places is 4.217163. It is the real solution of the equation x³ = 75. The cube root of 75 is expressed as ∛75 in the radical form and as (75)^⅓ or (75)^0.33 in the exponent form. The prime factorization of 75 is 3 × 5 × 5, hence, the cube root of 75 in its lowest radical form is expressed as ∛75.

Cube root of 75: 4.217163327
Cube root of 75 in Exponential Form: (75)^⅓
Cube root of 75 in Radical Form: ∛75

1.	What is the Cube Root of 75?
2.	How to Calculate the Cube Root of 75?
3.	Is the Cube Root of 75 Irrational?
4.	FAQs on Cube Root of 75

What is the Cube Root of 75?

The cube root of 75 is the number which when multiplied by itself three times gives the product as 75. Since 75 can be expressed as 3 × 5 × 5. Therefore, the cube root of 75 = ∛(3 × 5 × 5) = 4.2172.

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How to Calculate the Value of the Cube Root of 75?

Cube Root of 75 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 = 75
Let us assume x as 4
[∵ 4³ = 64 and 64 is the nearest perfect cube that is less than 75]
⇒ x = 4
Therefore,
∛75 = 4 (4³ + 2 × 75)/(2 × 4³ + 75)) = 4.22
⇒ ∛75 ≈ 4.22
Therefore, the cube root of 75 is 4.22 approximately.

Is the Cube Root of 75 Irrational?

Yes, because ∛75 = ∛(3 × 5 × 5) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 75 is an irrational number.

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Cube Root of 75 Solved Examples

Example 1: Given the volume of a cube is 75 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 75 in³ = a³
⇒ a³ = 75
Cube rooting on both sides,
⇒ a = ∛75 in
Since the cube root of 75 is 4.22, therefore, the length of the side of the cube is 4.22 in.
Example 2: The volume of a spherical ball is 75π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 75π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 75
⇒ R = ∛(3/4 × 75) = ∛(3/4) × ∛75 = 0.90856 × 4.21716 (∵ ∛(3/4) = 0.90856 and ∛75 = 4.21716)
⇒ R = 3.83154 in³
Example 3: What is the value of ∛75 + ∛(-75)?

Solution:

The cube root of -75 is equal to the negative of the cube root of 75.
i.e. ∛-75 = -∛75

Therefore, ∛75 + ∛(-75) = ∛75 - ∛75 = 0

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FAQs on Cube Root of 75

What is the Value of the Cube Root of 75?

We can express 75 as 3 × 5 × 5 i.e. ∛75 = ∛(3 × 5 × 5) = 4.21716. Therefore, the value of the cube root of 75 is 4.21716.

What is the Value of 10 Plus 9 Cube Root 75?

The value of ∛75 is 4.217. So, 10 + 9 × ∛75 = 10 + 9 × 4.217 = 47.952999999999996. Hence, the value of 10 plus 9 cube root 75 is 47.952999999999996.

How to Simplify the Cube Root of 75/125?

We know that the cube root of 75 is 4.21716 and the cube root of 125 is 5. Therefore, ∛(75/125) = (∛75)/(∛125) = 4.217/5 = 0.8434.

Is 75 a Perfect Cube?

The number 75 on prime factorization gives 3 × 5 × 5. Here, the prime factor 3 is not in the power of 3. Therefore the cube root of 75 is irrational, hence 75 is not a perfect cube.

What is the Cube of the Cube Root of 75?

The cube of the cube root of 75 is the number 75 itself i.e. (∛75)³ = (75^1/3)³ = 75.

What is the Cube Root of -75?

The cube root of -75 is equal to the negative of the cube root of 75. Therefore, ∛-75 = -(∛75) = -(4.217) = -4.217.