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Cube Root of 2025

The value of the cube root of 2025 rounded to 6 decimal places is 12.65149. It is the real solution of the equation x³ = 2025. The cube root of 2025 is expressed as ∛2025 or 3 ∛75 in the radical form and as (2025)^⅓ or (2025)^0.33 in the exponent form. The prime factorization of 2025 is 3 × 3 × 3 × 3 × 5 × 5, hence, the cube root of 2025 in its lowest radical form is expressed as 3 ∛75.

Cube root of 2025: 12.65148998
Cube root of 2025 in Exponential Form: (2025)^⅓
Cube root of 2025 in Radical Form: ∛2025 or 3 ∛75

Cube Root of 2025

1.	What is the Cube Root of 2025?
2.	How to Calculate the Cube Root of 2025?
3.	Is the Cube Root of 2025 Irrational?
4.	FAQs on Cube Root of 2025

What is the Cube Root of 2025?

The cube root of 2025 is the number which when multiplied by itself three times gives the product as 2025. Since 2025 can be expressed as 3 × 3 × 3 × 3 × 5 × 5. Therefore, the cube root of 2025 = ∛(3 × 3 × 3 × 3 × 5 × 5) = 12.6515.

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How to Calculate the Value of the Cube Root of 2025?

Cube Root of 2025 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 = 2025
Let us assume x as 12
[∵ 12³ = 1728 and 1728 is the nearest perfect cube that is less than 2025]
⇒ x = 12
Therefore,
∛2025 = 12 (12³ + 2 × 2025)/(2 × 12³ + 2025)) = 12.65
⇒ ∛2025 ≈ 12.65
Therefore, the cube root of 2025 is 12.65 approximately.

Is the Cube Root of 2025 Irrational?

Yes, because ∛2025 = ∛(3 × 3 × 3 × 3 × 5 × 5) = 3 ∛75 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 2025 is an irrational number.

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Cube Root of 2025 Solved Examples

Example 1: Find the real root of the equation x³ − 2025 = 0.

Solution:

x³ − 2025 = 0 i.e. x³ = 2025
Solving for x gives us,
x = ∛2025, x = ∛2025 × (-1 + √3i))/2 and x = ∛2025 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛2025
Therefore, the real root of the equation x³ − 2025 = 0 is for x = ∛2025 = 12.6515.
Example 2: What is the value of ∛2025 ÷ ∛(-2025)?

Solution:

The cube root of -2025 is equal to the negative of the cube root of 2025.
⇒ ∛-2025 = -∛2025

Therefore,
⇒ ∛2025/∛(-2025) = ∛2025/(-∛2025) = -1
Example 3: Given the volume of a cube is 2025 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 2025 in³ = a³
⇒ a³ = 2025
Cube rooting on both sides,
⇒ a = ∛2025 in
Since the cube root of 2025 is 12.65, therefore, the length of the side of the cube is 12.65 in.

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FAQs on Cube Root of 2025

What is the Value of the Cube Root of 2025?

We can express 2025 as 3 × 3 × 3 × 3 × 5 × 5 i.e. ∛2025 = ∛(3 × 3 × 3 × 3 × 5 × 5) = 12.65149. Therefore, the value of the cube root of 2025 is 12.65149.

How to Simplify the Cube Root of 2025/27?

We know that the cube root of 2025 is 12.65149 and the cube root of 27 is 3. Therefore, ∛(2025/27) = (∛2025)/(∛27) = 12.651/3 = 4.217.

What is the Value of 5 Plus 7 Cube Root 2025?

The value of ∛2025 is 12.651. So, 5 + 7 × ∛2025 = 5 + 7 × 12.651 = 93.557. Hence, the value of 5 plus 7 cube root 2025 is 93.557.

What is the Cube of the Cube Root of 2025?

The cube of the cube root of 2025 is the number 2025 itself i.e. (∛2025)³ = (2025^1/3)³ = 2025.

Is 2025 a Perfect Cube?

The number 2025 on prime factorization gives 3 × 3 × 3 × 3 × 5 × 5. Here, the prime factor 3 is not in the power of 3. Therefore the cube root of 2025 is irrational, hence 2025 is not a perfect cube.

If the Cube Root of 2025 is 12.65, Find the Value of ∛2.025.

Let us represent ∛2.025 in p/q form i.e. ∛(2025/1000) = 12.65/10 = 1.27. Hence, the value of ∛2.025 = 1.27.

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