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Cube Root of 53

The value of the cube root of 53 rounded to 6 decimal places is 3.756286. It is the real solution of the equation x³ = 53. The cube root of 53 is expressed as ∛53 in the radical form and as (53)^⅓ or (53)^0.33 in the exponent form. The prime factorization of 53 is 53, hence, the cube root of 53 in its lowest radical form is expressed as ∛53.

Cube root of 53: 3.756285754
Cube root of 53 in Exponential Form: (53)^⅓
Cube root of 53 in Radical Form: ∛53

Cube Root of 53

1.	What is the Cube Root of 53?
2.	How to Calculate the Cube Root of 53?
3.	Is the Cube Root of 53 Irrational?
4.	FAQs on Cube Root of 53

What is the Cube Root of 53?

The cube root of 53 is the number which when multiplied by itself three times gives the product as 53. The number 53 is prime. Therefore, the cube root of 53 = ∛53 = 3.7563.

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How to Calculate the Value of the Cube Root of 53?

Cube Root of 53 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 = 53
Let us assume x as 3
[∵ 3³ = 27 and 27 is the nearest perfect cube that is less than 53]
⇒ x = 3
Therefore,
∛53 = 3 (3³ + 2 × 53)/(2 × 3³ + 53)) = 3.73
⇒ ∛53 ≈ 3.73
Therefore, the cube root of 53 is 3.73 approximately.

Is the Cube Root of 53 Irrational?

Yes, because ∛53 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 53 is an irrational number.

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Cube Root of 53 Solved Examples

Example 1: The volume of a spherical ball is 53π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 53π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 53
⇒ R = ∛(3/4 × 53) = ∛(3/4) × ∛53 = 0.90856 × 3.75629 (∵ ∛(3/4) = 0.90856 and ∛53 = 3.75629)
⇒ R = 3.41281 in³
Example 2: Find the real root of the equation x³ − 53 = 0.

Solution:

x³ − 53 = 0 i.e. x³ = 53
Solving for x gives us,
x = ∛53, x = ∛53 × (-1 + √3i))/2 and x = ∛53 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛53
Therefore, the real root of the equation x³ − 53 = 0 is for x = ∛53 = 3.7563.
Example 3: What is the value of ∛53 ÷ ∛(-53)?

Solution:

The cube root of -53 is equal to the negative of the cube root of 53.
⇒ ∛-53 = -∛53

Therefore,
⇒ ∛53/∛(-53) = ∛53/(-∛53) = -1

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FAQs on Cube Root of 53

What is the Value of the Cube Root of 53?

The value of the cube root of 53 is 3.75629.

What is the Cube Root of -53?

The cube root of -53 is equal to the negative of the cube root of 53. Therefore, ∛-53 = -(∛53) = -(3.756) = -3.756.

Is 53 a Perfect Cube?

The number 53 is prime. Here, the prime factor 53 is not in the power of 3 and this implies that the cube root of 53 is irrational, hence 53 is not a perfect cube.

If the Cube Root of 53 is 3.76, Find the Value of ∛0.053.

Let us represent ∛0.053 in p/q form i.e. ∛(53/1000) = 3.76/10 = 0.38. Hence, the value of ∛0.053 = 0.38.

What is the Cube of the Cube Root of 53?

The cube of the cube root of 53 is the number 53 itself i.e. (∛53)³ = (53^1/3)³ = 53.

Why is the Value of the Cube Root of 53 Irrational?

The value of the cube root of 53 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛53 is irrational.

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