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Cube Root of 1512

The value of the cube root of 1512 rounded to 5 decimal places is 11.47759. It is the real solution of the equation x3 = 1512. The cube root of 1512 is expressed as ∛1512 or 6 ∛7 in the radical form and as (1512)⅓ or (1512)0.33 in the exponent form. The prime factorization of 1512 is 2 × 2 × 2 × 3 × 3 × 3 × 7, hence, the cube root of 1512 in its lowest radical form is expressed as 6 ∛7.

  • Cube root of 1512: 11.477587097
  • Cube root of 1512 in Exponential Form: (1512)⅓
  • Cube root of 1512 in Radical Form: ∛1512 or 6 ∛7

Cube Root of 1512

1. What is the Cube Root of 1512?
2. How to Calculate the Cube Root of 1512?
3. Is the Cube Root of 1512 Irrational?
4. FAQs on Cube Root of 1512

What is the Cube Root of 1512?

The cube root of 1512 is the number which when multiplied by itself three times gives the product as 1512. Since 1512 can be expressed as 2 × 2 × 2 × 3 × 3 × 3 × 7. Therefore, the cube root of 1512 = ∛(2 × 2 × 2 × 3 × 3 × 3 × 7) = 11.4776.

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How to Calculate the Value of the Cube Root of 1512?

Cube Root of 1512 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 = 1512
Let us assume x as 11
[∵ 113 = 1331 and 1331 is the nearest perfect cube that is less than 1512]
⇒ x = 11
Therefore,
∛1512 = 11 (113 + 2 × 1512)/(2 × 113 + 1512)) = 11.48
⇒ ∛1512 ≈ 11.48
Therefore, the cube root of 1512 is 11.48 approximately.

Is the Cube Root of 1512 Irrational?

Yes, because ∛1512 = ∛(2 × 2 × 2 × 3 × 3 × 3 × 7) = 6 ∛7 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 1512 is an irrational number.

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Cube Root of 1512 Solved Examples

  1. Example 1: Given the volume of a cube is 1512 in3. Find the length of the side of the cube.

    Solution:

    Volume of the Cube = 1512 in3 = a3
    ⇒ a3 = 1512
    Cube rooting on both sides,
    ⇒ a = ∛1512 in
    Since the cube root of 1512 is 11.48, therefore, the length of the side of the cube is 11.48 in.

  2. Example 2: What is the value of ∛1512 + ∛(-1512)?

    Solution:

    The cube root of -1512 is equal to the negative of the cube root of 1512.
    i.e. ∛-1512 = -∛1512

    Therefore, ∛1512 + ∛(-1512) = ∛1512 - ∛1512 = 0

  3. Example 3: Find the real root of the equation x3 − 1512 = 0.

    Solution:

    x3 − 1512 = 0 i.e. x3 = 1512
    Solving for x gives us,
    x = ∛1512, x = ∛1512 × (-1 + √3i))/2 and x = ∛1512 × (-1 - √3i))/2
    where i is called the imaginary unit and is equal to √-1.
    Ignoring imaginary roots,
    x = ∛1512
    Therefore, the real root of the equation x3 − 1512 = 0 is for x = ∛1512 = 11.4776.

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FAQs on Cube Root of 1512

What is the Value of the Cube Root of 1512?

We can express 1512 as 2 × 2 × 2 × 3 × 3 × 3 × 7 i.e. ∛1512 = ∛(2 × 2 × 2 × 3 × 3 × 3 × 7) = 11.47759. Therefore, the value of the cube root of 1512 is 11.47759.

How to Simplify the Cube Root of 1512/27?

We know that the cube root of 1512 is 11.47759 and the cube root of 27 is 3. Therefore, ∛(1512/27) = (∛1512)/(∛27) = 11.478/3 = 3.826.

Is 1512 a Perfect Cube?

The number 1512 on prime factorization gives 2 × 2 × 2 × 3 × 3 × 3 × 7. Here, the prime factor 7 is not in the power of 3. Therefore the cube root of 1512 is irrational, hence 1512 is not a perfect cube.

Why is the Value of the Cube Root of 1512 Irrational?

The value of the cube root of 1512 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛1512 is irrational.

If the Cube Root of 1512 is 11.48, Find the Value of ∛1.512.

Let us represent ∛1.512 in p/q form i.e. ∛(1512/1000) = 11.48/10 = 1.15. Hence, the value of ∛1.512 = 1.15.

What is the Cube Root of -1512?

The cube root of -1512 is equal to the negative of the cube root of 1512. Therefore, ∛-1512 = -(∛1512) = -(11.478) = -11.478.

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