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Cube Root of 63

The value of the cube root of 63 rounded to 4 decimal places is 3.9791. It is the real solution of the equation x3 = 63. The cube root of 63 is expressed as ∛63 in the radical form and as (63)⅓ or (63)0.33 in the exponent form. The prime factorization of 63 is 3 × 3 × 7, hence, the cube root of 63 in its lowest radical form is expressed as ∛63.

  • Cube root of 63: 3.979057208
  • Cube root of 63 in Exponential Form: (63)⅓
  • Cube root of 63 in Radical Form: ∛63

Cube Root of 63

1. What is the Cube Root of 63?
2. How to Calculate the Cube Root of 63?
3. Is the Cube Root of 63 Irrational?
4. FAQs on Cube Root of 63

What is the Cube Root of 63?

The cube root of 63 is the number which when multiplied by itself three times gives the product as 63. Since 63 can be expressed as 3 × 3 × 7. Therefore, the cube root of 63 = ∛(3 × 3 × 7) = 3.9791.

☛ Check: Cube Root Calculator

How to Calculate the Value of the Cube Root of 63?

Cube Root of 63 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 = 63
Let us assume x as 3
[∵ 33 = 27 and 27 is the nearest perfect cube that is less than 63]
⇒ x = 3
Therefore,
∛63 = 3 (33 + 2 × 63)/(2 × 33 + 63)) = 3.92
⇒ ∛63 ≈ 3.92
Therefore, the cube root of 63 is 3.92 approximately.

Is the Cube Root of 63 Irrational?

Yes, because ∛63 = ∛(3 × 3 × 7) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 63 is an irrational number.

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Cube Root of 63 Solved Examples

  1. Example 1: Find the real root of the equation x3 − 63 = 0.

    Solution:

    x3 − 63 = 0 i.e. x3 = 63
    Solving for x gives us,
    x = ∛63, x = ∛63 × (-1 + √3i))/2 and x = ∛63 × (-1 - √3i))/2
    where i is called the imaginary unit and is equal to √-1.
    Ignoring imaginary roots,
    x = ∛63
    Therefore, the real root of the equation x3 − 63 = 0 is for x = ∛63 = 3.9791.

  2. Example 2: Given the volume of a cube is 63 in3. Find the length of the side of the cube.

    Solution:

    Volume of the Cube = 63 in3 = a3
    ⇒ a3 = 63
    Cube rooting on both sides,
    ⇒ a = ∛63 in
    Since the cube root of 63 is 3.98, therefore, the length of the side of the cube is 3.98 in.

  3. Example 3: What is the value of ∛63 ÷ ∛(-63)?

    Solution:

    The cube root of -63 is equal to the negative of the cube root of 63.
    ⇒ ∛-63 = -∛63

    Therefore,
    ⇒ ∛63/∛(-63) = ∛63/(-∛63) = -1

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FAQs on Cube Root of 63

What is the Value of the Cube Root of 63?

We can express 63 as 3 × 3 × 7 i.e. ∛63 = ∛(3 × 3 × 7) = 3.97906. Therefore, the value of the cube root of 63 is 3.97906.

What is the Cube Root of -63?

The cube root of -63 is equal to the negative of the cube root of 63. Therefore, ∛-63 = -(∛63) = -(3.979) = -3.979.

What is the Cube of the Cube Root of 63?

The cube of the cube root of 63 is the number 63 itself i.e. (∛63)3 = (631/3)3 = 63.

Why is the Value of the Cube Root of 63 Irrational?

The value of the cube root of 63 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛63 is irrational.

How to Simplify the Cube Root of 63/64?

We know that the cube root of 63 is 3.97906 and the cube root of 64 is 4. Therefore, ∛(63/64) = (∛63)/(∛64) = 3.979/4 = 0.9948.

Is 63 a Perfect Cube?

The number 63 on prime factorization gives 3 × 3 × 7. Here, the prime factor 3 is not in the power of 3. Therefore the cube root of 63 is irrational, hence 63 is not a perfect cube.

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