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Cube Root of 25

The value of the cube root of 25 rounded to 6 decimal places is 2.924018. It is the real solution of the equation x³ = 25. The cube root of 25 is expressed as ∛25 in the radical form and as (25)^⅓ or (25)^0.33 in the exponent form. The prime factorization of 25 is 5 × 5, hence, the cube root of 25 in its lowest radical form is expressed as ∛25.

Cube root of 25: 2.924017738
Cube root of 25 in Exponential Form: (25)^⅓
Cube root of 25 in Radical Form: ∛25

1.	What is the Cube Root of 25?
2.	How to Calculate the Cube Root of 25?
3.	Is the Cube Root of 25 Irrational?
4.	FAQs on Cube Root of 25

What is the Cube Root of 25?

The cube root of 25 is the number which when multiplied by itself three times gives the product as 25. Since 25 can be expressed as 5 × 5. Therefore, the cube root of 25 = ∛(5 × 5) = 2.924.

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How to Calculate the Value of the Cube Root of 25?

Cube Root of 25 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 = 25
Let us assume x as 2
[∵ 2³ = 8 and 8 is the nearest perfect cube that is less than 25]
⇒ x = 2
Therefore,
∛25 = 2 (2³ + 2 × 25)/(2 × 2³ + 25)) = 2.83
⇒ ∛25 ≈ 2.83
Therefore, the cube root of 25 is 2.83 approximately.

Is the Cube Root of 25 Irrational?

Yes, because ∛25 = ∛(5 × 5) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 25 is an irrational number.

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Cube Root of 25 Solved Examples

Example 1: The volume of a spherical ball is 25π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 25π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 25
⇒ R = ∛(3/4 × 25) = ∛(3/4) × ∛25 = 0.90856 × 2.92402 (∵ ∛(3/4) = 0.90856 and ∛25 = 2.92402)
⇒ R = 2.65665 in³
Example 2: Given the volume of a cube is 25 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 25 in³ = a³
⇒ a³ = 25
Cube rooting on both sides,
⇒ a = ∛25 in
Since the cube root of 25 is 2.92, therefore, the length of the side of the cube is 2.92 in.
Example 3: What is the value of ∛25 + ∛(-25)?

Solution:

The cube root of -25 is equal to the negative of the cube root of 25.
i.e. ∛-25 = -∛25

Therefore, ∛25 + ∛(-25) = ∛25 - ∛25 = 0

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FAQs on Cube Root of 25

What is the Value of the Cube Root of 25?

We can express 25 as 5 × 5 i.e. ∛25 = ∛(5 × 5) = 2.92402. Therefore, the value of the cube root of 25 is 2.92402.

What is the Cube Root of -25?

The cube root of -25 is equal to the negative of the cube root of 25. Therefore, ∛-25 = -(∛25) = -(2.924) = -2.924.

Is 25 a Perfect Cube?

The number 25 on prime factorization gives 5 × 5. Here, the prime factor 5 is not in the power of 3. Therefore the cube root of 25 is irrational, hence 25 is not a perfect cube.

If the Cube Root of 25 is 2.92, Find the Value of ∛0.025.

Let us represent ∛0.025 in p/q form i.e. ∛(25/1000) = 2.92/10 = 0.29. Hence, the value of ∛0.025 = 0.29.

How to Simplify the Cube Root of 25/343?

We know that the cube root of 25 is 2.92402 and the cube root of 343 is 7. Therefore, ∛(25/343) = (∛25)/(∛343) = 2.924/7 = 0.4177.

Why is the Value of the Cube Root of 25 Irrational?

The value of the cube root of 25 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛25 is irrational.