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Cube Root of 7

The value of the cube root of 7 rounded to 6 decimal places is 1.912931. It is the real solution of the equation x3 = 7. The cube root of 7 is expressed as ∛7 in the radical form and as (7)⅓ or (7)0.33 in the exponent form. The prime factorization of 7 is 7, hence, the cube root of 7 in its lowest radical form is expressed as ∛7.

  • Cube root of 7: 1.912931183
  • Cube root of 7 in Exponential Form: (7)⅓
  • Cube root of 7 in Radical Form: ∛7

Cube Root of 7

1. What is the Cube Root of 7?
2. How to Calculate the Cube Root of 7?
3. Is the Cube Root of 7 Irrational?
4. FAQs on Cube Root of 7

What is the Cube Root of 7?

The cube root of 7 is the number which when multiplied by itself three times gives the product as 7. The number 7 is prime. Therefore, the cube root of 7 = ∛7 = 1.9129.

☛ Check: Cube Root Calculator

How to Calculate the Value of the Cube Root of 7?

Cube Root of 7 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 = 7
Let us assume x as 1
[∵ 13 = 1 and 1 is the nearest perfect cube that is less than 7]
⇒ x = 1
Therefore,
∛7 = 1 (13 + 2 × 7)/(2 × 13 + 7)) = 1.67
⇒ ∛7 ≈ 1.67
Therefore, the cube root of 7 is 1.67 approximately.

Is the Cube Root of 7 Irrational?

Yes, because ∛7 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 7 is an irrational number.

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Cube Root of 7 Solved Examples

  1. Example 1: Find the real root of the equation x3 − 7 = 0.

    Solution:

    x3 − 7 = 0 i.e. x3 = 7
    Solving for x gives us,
    x = ∛7, x = ∛7 × (-1 + √3i))/2 and x = ∛7 × (-1 - √3i))/2
    where i is called the imaginary unit and is equal to √-1.
    Ignoring imaginary roots,
    x = ∛7
    Therefore, the real root of the equation x3 − 7 = 0 is for x = ∛7 = 1.9129.

  2. Example 2: The volume of a spherical ball is 7π in3. What is the radius of this ball?

    Solution:

    Volume of the spherical ball = 7π in3
    = 4/3 × π × R3
    ⇒ R3 = 3/4 × 7
    ⇒ R = ∛(3/4 × 7) = ∛(3/4) × ∛7 = 0.90856 × 1.91293 (∵ ∛(3/4) = 0.90856 and ∛7 = 1.91293)
    ⇒ R = 1.73801 in3

  3. Example 3: Given the volume of a cube is 7 in3. Find the length of the side of the cube.

    Solution:

    Volume of the Cube = 7 in3 = a3
    ⇒ a3 = 7
    Cube rooting on both sides,
    ⇒ a = ∛7 in
    Since the cube root of 7 is 1.91, therefore, the length of the side of the cube is 1.91 in.

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FAQs on Cube Root of 7

What is the Value of the Cube Root of 7?

The value of the cube root of 7 is 1.91293.

If the Cube Root of 7 is 1.91, Find the Value of ∛0.007.

Let us represent ∛0.007 in p/q form i.e. ∛(7/1000) = 1.91/10 = 0.19. Hence, the value of ∛0.007 = 0.19.

What is the Cube of the Cube Root of 7?

The cube of the cube root of 7 is the number 7 itself i.e. (∛7)3 = (71/3)3 = 7.

Why is the Value of the Cube Root of 7 Irrational?

The value of the cube root of 7 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛7 is irrational.

Is 7 a Perfect Cube?

The number 7 is prime. Here, the prime factor 7 is not in the power of 3 and this implies that the cube root of 7 is irrational, hence 7 is not a perfect cube.

How to Simplify the Cube Root of 7/125?

We know that the cube root of 7 is 1.91293 and the cube root of 125 is 5. Therefore, ∛(7/125) = (∛7)/(∛125) = 1.913/5 = 0.3826.

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