Answer:
2.5
Step-by-step explanation:
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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
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?
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Is 18 a Perfect Cube?
Why is the Value of the Cube Root of 18 Irrational?
If the Cube Root of 18 is 2.62, Find the Value of ∛0.018 .