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Cube Root of 35

The value of the cube root of 35 rounded to 5 decimal places is 3.27107. It is the real solution of the equation x3 = 35. The cube root of 35 is expressed as ∛35 in the radical form and as (35)⅓ or (35)0.33 in the exponent form. The prime factorization of 35 is 5 × 7, hence, the cube root of 35 in its lowest radical form is expressed as ∛35.

  • Cube root of 35: 3.27106631
  • Cube root of 35 in Exponential Form: (35)⅓
  • Cube root of 35 in Radical Form: ∛35

Cube Root of 35

1. What is the Cube Root of 35?
2. How to Calculate the Cube Root of 35?
3. Is the Cube Root of 35 Irrational?
4. FAQs on Cube Root of 35

What is the Cube Root of 35?

The cube root of 35 is the number which when multiplied by itself three times gives the product as 35. Since 35 can be expressed as 5 × 7. Therefore, the cube root of 35 = ∛(5 × 7) = 3.2711.

☛ Check: Cube Root Calculator

How to Calculate the Value of the Cube Root of 35?

Cube Root of 35 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 = 35
Let us assume x as 3
[∵ 33 = 27 and 27 is the nearest perfect cube that is less than 35]
⇒ x = 3
Therefore,
∛35 = 3 (33 + 2 × 35)/(2 × 33 + 35)) = 3.27
⇒ ∛35 ≈ 3.27
Therefore, the cube root of 35 is 3.27 approximately.

Is the Cube Root of 35 Irrational?

Yes, because ∛35 = ∛(5 × 7) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 35 is an irrational number.

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Cube Root of 35 Solved Examples

  1. Example 1: What is the value of ∛35 + ∛(-35)?

    Solution:

    The cube root of -35 is equal to the negative of the cube root of 35.
    i.e. ∛-35 = -∛35

    Therefore, ∛35 + ∛(-35) = ∛35 - ∛35 = 0

  2. Example 2: Find the real root of the equation x3 − 35 = 0.

    Solution:

    x3 − 35 = 0 i.e. x3 = 35
    Solving for x gives us,
    x = ∛35, x = ∛35 × (-1 + √3i))/2 and x = ∛35 × (-1 - √3i))/2
    where i is called the imaginary unit and is equal to √-1.
    Ignoring imaginary roots,
    x = ∛35
    Therefore, the real root of the equation x3 − 35 = 0 is for x = ∛35 = 3.2711.

  3. Example 3: Given the volume of a cube is 35 in3. Find the length of the side of the cube.

    Solution:

    Volume of the Cube = 35 in3 = a3
    ⇒ a3 = 35
    Cube rooting on both sides,
    ⇒ a = ∛35 in
    Since the cube root of 35 is 3.27, therefore, the length of the side of the cube is 3.27 in.

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FAQs on Cube Root of 35

What is the Value of the Cube Root of 35?

We can express 35 as 5 × 7 i.e. ∛35 = ∛(5 × 7) = 3.27107. Therefore, the value of the cube root of 35 is 3.27107.

How to Simplify the Cube Root of 35/8?

We know that the cube root of 35 is 3.27107 and the cube root of 8 is 2. Therefore, ∛(35/8) = (∛35)/(∛8) = 3.271/2 = 1.6355.

Is 35 a Perfect Cube?

The number 35 on prime factorization gives 5 × 7. Here, the prime factor 5 is not in the power of 3. Therefore the cube root of 35 is irrational, hence 35 is not a perfect cube.

If the Cube Root of 35 is 3.27, Find the Value of ∛0.035.

Let us represent ∛0.035 in p/q form i.e. ∛(35/1000) = 3.27/10 = 0.33. Hence, the value of ∛0.035 = 0.33.

What is the Cube of the Cube Root of 35?

The cube of the cube root of 35 is the number 35 itself i.e. (∛35)3 = (351/3)3 = 35.

What is the Cube Root of -35?

The cube root of -35 is equal to the negative of the cube root of 35. Therefore, ∛-35 = -(∛35) = -(3.271) = -3.271.

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