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Cube Root of 375

The value of the cube root of 375 rounded to 7 decimal places is 7.2112479. It is the real solution of the equation x³ = 375. The cube root of 375 is expressed as ∛375 or 5 ∛3 in the radical form and as (375)^⅓ or (375)^0.33 in the exponent form. The prime factorization of 375 is 3 × 5 × 5 × 5, hence, the cube root of 375 in its lowest radical form is expressed as 5 ∛3.

Cube root of 375: 7.211247852
Cube root of 375 in Exponential Form: (375)^⅓
Cube root of 375 in Radical Form: ∛375 or 5 ∛3

1.	What is the Cube Root of 375?
2.	How to Calculate the Cube Root of 375?
3.	Is the Cube Root of 375 Irrational?
4.	FAQs on Cube Root of 375

What is the Cube Root of 375?

The cube root of 375 is the number which when multiplied by itself three times gives the product as 375. Since 375 can be expressed as 3 × 5 × 5 × 5. Therefore, the cube root of 375 = ∛(3 × 5 × 5 × 5) = 7.2112.

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How to Calculate the Value of the Cube Root of 375?

Cube Root of 375 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 = 375
Let us assume x as 7
[∵ 7³ = 343 and 343 is the nearest perfect cube that is less than 375]
⇒ x = 7
Therefore,
∛375 = 7 (7³ + 2 × 375)/(2 × 7³ + 375)) = 7.21
⇒ ∛375 ≈ 7.21
Therefore, the cube root of 375 is 7.21 approximately.

Is the Cube Root of 375 Irrational?

Yes, because ∛375 = ∛(3 × 5 × 5 × 5) = 5 ∛3 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 375 is an irrational number.

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Cube Root of 375 Solved Examples

Example 1: What is the value of ∛375 + ∛(-375)?

Solution:

The cube root of -375 is equal to the negative of the cube root of 375.
i.e. ∛-375 = -∛375

Therefore, ∛375 + ∛(-375) = ∛375 - ∛375 = 0
Example 2: Given the volume of a cube is 375 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 375 in³ = a³
⇒ a³ = 375
Cube rooting on both sides,
⇒ a = ∛375 in
Since the cube root of 375 is 7.21, therefore, the length of the side of the cube is 7.21 in.
Example 3: The volume of a spherical ball is 375π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 375π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 375
⇒ R = ∛(3/4 × 375) = ∛(3/4) × ∛375 = 0.90856 × 7.21125 (∵ ∛(3/4) = 0.90856 and ∛375 = 7.21125)
⇒ R = 6.55185 in³

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FAQs on Cube Root of 375

What is the Value of the Cube Root of 375?

We can express 375 as 3 × 5 × 5 × 5 i.e. ∛375 = ∛(3 × 5 × 5 × 5) = 7.21125. Therefore, the value of the cube root of 375 is 7.21125.

What is the Cube of the Cube Root of 375?

The cube of the cube root of 375 is the number 375 itself i.e. (∛375)³ = (375^1/3)³ = 375.

How to Simplify the Cube Root of 375/216?

We know that the cube root of 375 is 7.21125 and the cube root of 216 is 6. Therefore, ∛(375/216) = (∛375)/(∛216) = 7.211/6 = 1.2018.

Why is the Value of the Cube Root of 375 Irrational?

The value of the cube root of 375 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛375 is irrational.

Is 375 a Perfect Cube?

The number 375 on prime factorization gives 3 × 5 × 5 × 5. Here, the prime factor 3 is not in the power of 3. Therefore the cube root of 375 is irrational, hence 375 is not a perfect cube.

If the Cube Root of 375 is 7.21, Find the Value of ∛0.375.

Let us represent ∛0.375 in p/q form i.e. ∛(375/1000) = 7.21/10 = 0.72. Hence, the value of ∛0.375 = 0.72.