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Square root of 36
Square root of 36

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Cube Root of 36

The value of the cube root of 36 rounded to 4 decimal places is 3.3019. It is the real solution of the equation x3 = 36. The cube root of 36 is expressed as ∛36 in the radical form and as (36)⅓ or (36)0.33 in the exponent form. The prime factorization of 36 is 2 × 2 × 3 × 3, hence, the cube root of 36 in its lowest radical form is expressed as ∛36.

  • Cube root of 36: 3.301927249
  • Cube root of 36 in Exponential Form: (36)⅓
  • Cube root of 36 in Radical Form: ∛36
1. What is the Cube Root of 36?
2. How to Calculate the Cube Root of 36?
3. Is the Cube Root of 36 Irrational?
4. FAQs on Cube Root of 36

What is the Cube Root of 36?

The cube root of 36 is the number which when multiplied by itself three times gives the product as 36. Since 36 can be expressed as 2 × 2 × 3 × 3. Therefore, the cube root of 36 = ∛(2 × 2 × 3 × 3) = 3.3019.

☛ Check: Cube Root Calculator

How to Calculate the Value of the Cube Root of 36?

Cube Root of 36 by Halley’s Method

Its formula is ∛a ≈ x ((x3 + 2a)/(2×3 + a))
where,
a = number whose cube root is being calculated
x = integer guess of its cube root.

Here a = 36
Let us assume x as 3
[∵ 33 = 27 and 27 is the nearest perfect cube that is less than 36]
⇒ x = 3
Therefore,
∛36 = 3 (33 + 2 × 36)/(2 × 33 + 36)) = 3.3
⇒ ∛36 ≈ 3.3
Therefore, the cube root of 36 is 3.3 approximately.

Is the Cube Root of 36 Irrational?

Yes, because ∛36 = ∛(2 × 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 36 is an irrational number.

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Cube Root of 36 Solved Examples

  1. Example 1: Given the volume of a cube is 36 in3. Find the length of the side of the cube.

    Solution:

    Volume of the Cube = 36 in3 = a3

    ⇒ a3 = 36
    Cube rooting on both sides,
    ⇒ a = ∛36 in
    Since the cube root of 36 is 3.3, therefore, the length of the side of the cube is 3.3 in.

  2. Example 2: What is the value of ∛36 ÷ ∛(-36)?

    Solution:

    The cube root of -36 is equal to the negative of the cube root of 36.

    ⇒ ∛-36 = -∛36
    Therefore,
    ⇒ ∛36/∛(-36) = ∛36/(-∛36) = -1

  3. Example 3: Find the real root of the equation x3 − 36 = 0.

    Solution:

    x3 − 36 = 0 i.e. x3 = 36

    Solving for x gives us,
    x = ∛36, x = ∛36 × (-1 + √3i))/2 and x = ∛36 × (-1 – √3i))/2
    where i is called the imaginary unit and is equal to √-1.
    Ignoring imaginary roots,
    x = ∛36
    Therefore, the real root of the equation x3 − 36 = 0 is for x = ∛36 = 3.3019.

FAQs on Cube Root of 36

What is the Value of the Cube Root of 36?

We can express 36 as 2 × 2 × 3 × 3 i.e. ∛36 = ∛(2 × 2 × 3 × 3) = 3.30193. Therefore, the value of the cube root of 36 is 3.30193.

Is 36 a Perfect Cube?

The number 36 on prime factorization gives 2 × 2 × 3 × 3. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 36 is irrational, hence 36 is not a perfect cube.

If the Cube Root of 36 is 3.3, Find the Value of ∛0.036.

Let us represent ∛0.036 in p/q form i.e. ∛(36/1000) = 3.3/10 = 0.33. Hence, the value of ∛0.036 = 0.33.

What is the Cube of the Cube Root of 36?

The cube of the cube root of 36 is the number 36 itself i.e. (∛36)3 = (361/3)3 = 36.

Why is the Value of the Cube Root of 36 Irrational?

The value of the cube root of 36 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛36 is irrational.

What is the Cube Root of -36?

The cube root of -36 is equal to the negative of the cube root of 36. Therefore, ∛-36 = -(∛36) = -(3.302) = -3.302.

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