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Cube Root of 18

The value of the cube root of 18 rounded to 4 decimal places is 2.6207. It is the real solution of the equation x³ = 18. The cube root of 18 is expressed as ∛18 in the radical form and as (18)^⅓ or (18)^0.33 in the exponent form. The prime factorization of 18 is 2 × 3 × 3, hence, the cube root of 18 in its lowest radical form is expressed as ∛18.

Cube root of 18: 2.620741394
Cube root of 18 in Exponential Form: (18)^⅓
Cube root of 18 in Radical Form: ∛18

Cube Root of 18

1.	What is the Cube Root of 18?
2.	How to Calculate the Cube Root of 18?
3.	Is the Cube Root of 18 Irrational?
4.	FAQs on Cube Root of 18

What is the Cube Root of 18?

The cube root of 18 is the number which when multiplied by itself three times gives the product as 18. Since 18 can be expressed as 2 × 3 × 3. Therefore, the cube root of 18 = ∛(2 × 3 × 3) = 2.6207.

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How to Calculate the Value of the Cube Root of 18?

Cube Root of 18 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 = 18
Let us assume x as 2
[∵ 2³ = 8 and 8 is the nearest perfect cube that is less than 18]
⇒ x = 2
Therefore,
∛18 = 2 (2³ + 2 × 18)/(2 × 2³ + 18)) = 2.59
⇒ ∛18 ≈ 2.59
Therefore, the cube root of 18 is 2.59 approximately.

Is the Cube Root of 18 Irrational?

Yes, because ∛18 = ∛(2 × 3 × 3) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 18 is an irrational number.

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Cube Root of 18 Solved Examples

Example 1: The volume of a spherical ball is 18π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 18π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 18
⇒ R = ∛(3/4 × 18) = ∛(3/4) × ∛18 = 0.90856 × 2.62074 (∵ ∛(3/4) = 0.90856 and ∛18 = 2.62074)
⇒ R = 2.3811 in³
Example 2: What is the value of ∛18 + ∛(-18)?

Solution:

The cube root of -18 is equal to the negative of the cube root of 18.
i.e. ∛-18 = -∛18

Therefore, ∛18 + ∛(-18) = ∛18 - ∛18 = 0
Example 3: Find the real root of the equation x³ − 18 = 0.

Solution:

x³ − 18 = 0 i.e. x³ = 18
Solving for x gives us,
x = ∛18, x = ∛18 × (-1 + √3i))/2 and x = ∛18 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛18
Therefore, the real root of the equation x³ − 18 = 0 is for x = ∛18 = 2.6207.

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FAQs on Cube Root of 18

What is the Value of the Cube Root of 18?

We can express 18 as 2 × 3 × 3 i.e. ∛18 = ∛(2 × 3 × 3) = 2.62074. Therefore, the value of the cube root of 18 is 2.62074.

What is the Value of 9 Plus 19 Cube Root 18?

The value of ∛18 is 2.621. So, 9 + 19 × ∛18 = 9 + 19 × 2.621 = 58.799. Hence, the value of 9 plus 19 cube root 18 is 58.799.

Is 18 a Perfect Cube?

The number 18 on prime factorization gives 2 × 3 × 3. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 18 is irrational, hence 18 is not a perfect cube.

Why is the Value of the Cube Root of 18 Irrational?

The value of the cube root of 18 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛18 is irrational.

If the Cube Root of 18 is 2.62, Find the Value of ∛0.018.

Let us represent ∛0.018 in p/q form i.e. ∛(18/1000) = 2.62/10 = 0.26. Hence, the value of ∛0.018 = 0.26.

How to Simplify the Cube Root of 18/512?

We know that the cube root of 18 is 2.62074 and the cube root of 512 is 8. Therefore, ∛(18/512) = (∛18)/(∛512) = 2.621/8 = 0.3276.

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