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Cube Root of 625

The value of the cube root of 625 rounded to 5 decimal places is 8.54988. It is the real solution of the equation x³ = 625. The cube root of 625 is expressed as ∛625 or 5 ∛5 in the radical form and as (625)^⅓ or (625)^0.33 in the exponent form. The prime factorization of 625 is 5 × 5 × 5 × 5, hence, the cube root of 625 in its lowest radical form is expressed as 5 ∛5.

Cube root of 625: 8.549879733
Cube root of 625 in Exponential Form: (625)^⅓
Cube root of 625 in Radical Form: ∛625 or 5 ∛5

Cube Root of 625

1.	What is the Cube Root of 625?
2.	How to Calculate the Cube Root of 625?
3.	Is the Cube Root of 625 Irrational?
4.	FAQs on Cube Root of 625

What is the Cube Root of 625?

The cube root of 625 is the number which when multiplied by itself three times gives the product as 625. Since 625 can be expressed as 5 × 5 × 5 × 5. Therefore, the cube root of 625 = ∛(5 × 5 × 5 × 5) = 8.5499.

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How to Calculate the Value of the Cube Root of 625?

Cube Root of 625 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 = 625
Let us assume x as 8
[∵ 8³ = 512 and 512 is the nearest perfect cube that is less than 625]
⇒ x = 8
Therefore,
∛625 = 8 (8³ + 2 × 625)/(2 × 8³ + 625)) = 8.55
⇒ ∛625 ≈ 8.55
Therefore, the cube root of 625 is 8.55 approximately.

Is the Cube Root of 625 Irrational?

Yes, because ∛625 = ∛(5 × 5 × 5 × 5) = 5 ∛5 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 625 is an irrational number.

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Cube Root of 625 Solved Examples

Example 1: The volume of a spherical ball is 625π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 625π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 625
⇒ R = ∛(3/4 × 625) = ∛(3/4) × ∛625 = 0.90856 × 8.54988 (∵ ∛(3/4) = 0.90856 and ∛625 = 8.54988)
⇒ R = 7.76808 in³
Example 2: What is the value of ∛625 ÷ ∛(-625)?

Solution:

The cube root of -625 is equal to the negative of the cube root of 625.
⇒ ∛-625 = -∛625

Therefore,
⇒ ∛625/∛(-625) = ∛625/(-∛625) = -1
Example 3: Find the real root of the equation x³ − 625 = 0.

Solution:

x³ − 625 = 0 i.e. x³ = 625
Solving for x gives us,
x = ∛625, x = ∛625 × (-1 + √3i))/2 and x = ∛625 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛625
Therefore, the real root of the equation x³ − 625 = 0 is for x = ∛625 = 8.5499.

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FAQs on Cube Root of 625

What is the Value of the Cube Root of 625?

We can express 625 as 5 × 5 × 5 × 5 i.e. ∛625 = ∛(5 × 5 × 5 × 5) = 8.54988. Therefore, the value of the cube root of 625 is 8.54988.

What is the Value of 16 Plus 1 Cube Root 625?

The value of ∛625 is 8.55. So, 16 + 1 × ∛625 = 16 + 1 × 8.55 = 24.55. Hence, the value of 16 plus 1 cube root 625 is 24.55.

How to Simplify the Cube Root of 625/8?

We know that the cube root of 625 is 8.54988 and the cube root of 8 is 2. Therefore, ∛(625/8) = (∛625)/(∛8) = 8.55/2 = 4.275.

Is 625 a Perfect Cube?

The number 625 on prime factorization gives 5 × 5 × 5 × 5. Here, the prime factor 5 is not in the power of 3. Therefore the cube root of 625 is irrational, hence 625 is not a perfect cube.

If the Cube Root of 625 is 8.55, Find the Value of ∛0.625.

Let us represent ∛0.625 in p/q form i.e. ∛(625/1000) = 8.55/10 = 0.85. Hence, the value of ∛0.625 = 0.85.

What is the Cube of the Cube Root of 625?

The cube of the cube root of 625 is the number 625 itself i.e. (∛625)³ = (625^1/3)³ = 625.

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