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Cube Root of 3456

The value of the cube root of 3456 rounded to 5 decimal places is 15.11905. It is the real solution of the equation x3 = 3456. The cube root of 3456 is expressed as ∛3456 or 12 ∛2 in the radical form and as (3456)⅓ or (3456)0.33 in the exponent form. The prime factorization of 3456 is 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3, hence, the cube root of 3456 in its lowest radical form is expressed as 12 ∛2.

  • Cube root of 3456: 15.119052599
  • Cube root of 3456 in Exponential Form: (3456)⅓
  • Cube root of 3456 in Radical Form: ∛3456 or 12 ∛2

Cube Root of 3456

1. What is the Cube Root of 3456?
2. How to Calculate the Cube Root of 3456?
3. Is the Cube Root of 3456 Irrational?
4. FAQs on Cube Root of 3456

What is the Cube Root of 3456?

The cube root of 3456 is the number which when multiplied by itself three times gives the product as 3456. Since 3456 can be expressed as 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3. Therefore, the cube root of 3456 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3) = 15.1191.

☛ Check: Cube Root Calculator

How to Calculate the Value of the Cube Root of 3456?

Cube Root of 3456 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 = 3456
Let us assume x as 15
[∵ 153 = 3375 and 3375 is the nearest perfect cube that is less than 3456]
⇒ x = 15
Therefore,
∛3456 = 15 (153 + 2 × 3456)/(2 × 153 + 3456)) = 15.12
⇒ ∛3456 ≈ 15.12
Therefore, the cube root of 3456 is 15.12 approximately.

Is the Cube Root of 3456 Irrational?

Yes, because ∛3456 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3) = 12 ∛2 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 3456 is an irrational number.

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Cube Root of 3456 Solved Examples

  1. Example 1: Given the volume of a cube is 3456 in3. Find the length of the side of the cube.

    Solution:

    Volume of the Cube = 3456 in3 = a3
    ⇒ a3 = 3456
    Cube rooting on both sides,
    ⇒ a = ∛3456 in
    Since the cube root of 3456 is 15.12, therefore, the length of the side of the cube is 15.12 in.

  2. Example 2: Find the real root of the equation x3 − 3456 = 0.

    Solution:

    x3 − 3456 = 0 i.e. x3 = 3456
    Solving for x gives us,
    x = ∛3456, x = ∛3456 × (-1 + √3i))/2 and x = ∛3456 × (-1 - √3i))/2
    where i is called the imaginary unit and is equal to √-1.
    Ignoring imaginary roots,
    x = ∛3456
    Therefore, the real root of the equation x3 − 3456 = 0 is for x = ∛3456 = 15.1191.

  3. Example 3: What is the value of ∛3456 ÷ ∛(-3456)?

    Solution:

    The cube root of -3456 is equal to the negative of the cube root of 3456.
    ⇒ ∛-3456 = -∛3456

    Therefore,
    ⇒ ∛3456/∛(-3456) = ∛3456/(-∛3456) = -1

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FAQs on Cube Root of 3456

What is the Value of the Cube Root of 3456?

We can express 3456 as 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 i.e. ∛3456 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3) = 15.11905. Therefore, the value of the cube root of 3456 is 15.11905.

How to Simplify the Cube Root of 3456/216?

We know that the cube root of 3456 is 15.11905 and the cube root of 216 is 6. Therefore, ∛(3456/216) = (∛3456)/(∛216) = 15.119/6 = 2.5198.

Why is the Value of the Cube Root of 3456 Irrational?

The value of the cube root of 3456 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛3456 is irrational.

What is the Cube Root of -3456?

The cube root of -3456 is equal to the negative of the cube root of 3456. Therefore, ∛-3456 = -(∛3456) = -(15.119) = -15.119.

What is the Cube of the Cube Root of 3456?

The cube of the cube root of 3456 is the number 3456 itself i.e. (∛3456)3 = (34561/3)3 = 3456.

What is the Value of 11 Plus 10 Cube Root 3456?

The value of ∛3456 is 15.119. So, 11 + 10 × ∛3456 = 11 + 10 × 15.119 = 162.19. Hence, the value of 11 plus 10 cube root 3456 is 162.19.

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