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Cube Root of 1458

The value of the cube root of 1458 rounded to 5 decimal places is 11.33929. It is the real solution of the equation x3 = 1458. The cube root of 1458 is expressed as ∛1458 or 9 ∛2 in the radical form and as (1458)⅓ or (1458)0.33 in the exponent form. The prime factorization of 1458 is 2 × 3 × 3 × 3 × 3 × 3 × 3, hence, the cube root of 1458 in its lowest radical form is expressed as 9 ∛2.

  • Cube root of 1458: 11.339289449
  • Cube root of 1458 in Exponential Form: (1458)⅓
  • Cube root of 1458 in Radical Form: ∛1458 or 9 ∛2

Cube Root of 1458

1. What is the Cube Root of 1458?
2. How to Calculate the Cube Root of 1458?
3. Is the Cube Root of 1458 Irrational?
4. FAQs on Cube Root of 1458

What is the Cube Root of 1458?

The cube root of 1458 is the number which when multiplied by itself three times gives the product as 1458. Since 1458 can be expressed as 2 × 3 × 3 × 3 × 3 × 3 × 3. Therefore, the cube root of 1458 = ∛(2 × 3 × 3 × 3 × 3 × 3 × 3) = 11.3393.

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How to Calculate the Value of the Cube Root of 1458?

Cube Root of 1458 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 = 1458
Let us assume x as 11
[∵ 113 = 1331 and 1331 is the nearest perfect cube that is less than 1458]
⇒ x = 11
Therefore,
∛1458 = 11 (113 + 2 × 1458)/(2 × 113 + 1458)) = 11.34
⇒ ∛1458 ≈ 11.34
Therefore, the cube root of 1458 is 11.34 approximately.

Is the Cube Root of 1458 Irrational?

Yes, because ∛1458 = ∛(2 × 3 × 3 × 3 × 3 × 3 × 3) = 9 ∛2 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 1458 is an irrational number.

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Cube Root of 1458 Solved Examples

  1. Example 1: The volume of a spherical ball is 1458π in3. What is the radius of this ball?

    Solution:

    Volume of the spherical ball = 1458π in3
    = 4/3 × π × R3
    ⇒ R3 = 3/4 × 1458
    ⇒ R = ∛(3/4 × 1458) = ∛(3/4) × ∛1458 = 0.90856 × 11.33929 (∵ ∛(3/4) = 0.90856 and ∛1458 = 11.33929)
    ⇒ R = 10.30243 in3

  2. Example 2: Find the real root of the equation x3 − 1458 = 0.

    Solution:

    x3 − 1458 = 0 i.e. x3 = 1458
    Solving for x gives us,
    x = ∛1458, x = ∛1458 × (-1 + √3i))/2 and x = ∛1458 × (-1 - √3i))/2
    where i is called the imaginary unit and is equal to √-1.
    Ignoring imaginary roots,
    x = ∛1458
    Therefore, the real root of the equation x3 − 1458 = 0 is for x = ∛1458 = 11.3393.

  3. Example 3: What is the value of ∛1458 ÷ ∛(-1458)?

    Solution:

    The cube root of -1458 is equal to the negative of the cube root of 1458.
    ⇒ ∛-1458 = -∛1458

    Therefore,
    ⇒ ∛1458/∛(-1458) = ∛1458/(-∛1458) = -1

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FAQs on Cube Root of 1458

What is the Value of the Cube Root of 1458?

We can express 1458 as 2 × 3 × 3 × 3 × 3 × 3 × 3 i.e. ∛1458 = ∛(2 × 3 × 3 × 3 × 3 × 3 × 3) = 11.33929. Therefore, the value of the cube root of 1458 is 11.33929.

What is the Value of 2 Plus 18 Cube Root 1458?

The value of ∛1458 is 11.339. So, 2 + 18 × ∛1458 = 2 + 18 × 11.339 = 206.102. Hence, the value of 2 plus 18 cube root 1458 is 206.102.

Why is the Value of the Cube Root of 1458 Irrational?

The value of the cube root of 1458 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛1458 is irrational.

Is 1458 a Perfect Cube?

The number 1458 on prime factorization gives 2 × 3 × 3 × 3 × 3 × 3 × 3. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 1458 is irrational, hence 1458 is not a perfect cube.

If the Cube Root of 1458 is 11.34, Find the Value of ∛1.458.

Let us represent ∛1.458 in p/q form i.e. ∛(1458/1000) = 11.34/10 = 1.13. Hence, the value of ∛1.458 = 1.13.

What is the Cube Root of -1458?

The cube root of -1458 is equal to the negative of the cube root of 1458. Therefore, ∛-1458 = -(∛1458) = -(11.339) = -11.339.

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