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Cube Root of 27

The value of the cube root of 27 is 3. It is the real solution of the equation x3 = 27. The cube root of 27 is expressed as ∛27 in radical form and as (27)⅓ or (27)0.33 in the exponent form. As the cube root of 27 is a whole number, 27 is a perfect cube.

  • Cube root of 27: 3
  • Cube root of 27 in exponential form: (27)⅓
  • Cube root of 27 in radical form: ∛27

Cube Root of 27

1. What is the Cube Root of 27?
2. How to Calculate the Cube Root of 27?
3. Is the Cube Root of 27 Irrational?
4. FAQs on Cube Root of 27

What is the Cube Root of 27?

The cube root of 27 is the number which when multiplied by itself three times gives the product as 27. Since 27 can be expressed as 3 × 3 × 3. Therefore, the cube root of 27 = ∛(3 × 3 × 3) = 3.

How to Calculate the Value of the Cube Root of 27?

Cube Root of 27 by Prime Factorization

  • Prime factorization of 27 is 3 × 3 × 3
  • Simplifying the above expression: 33

Therefore, the cube root of 27 by prime factorization is (3 × 3 × 3)1/3 = 3.

Is the Cube Root of 27 Irrational?

No, because ∛27 = ∛(3 × 3 × 3) can be expressed in the form of p/q i.e. 3/1. Therefore, the value of the cube root of 27 is an integer (rational).

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Cube Root of 27 Solved Examples

  1. Example 1: What is the value of ∛27 + ∛(-27)?

    Solution:

    The cube root of -27 is equal to the negative of the cube root of 27.
    i.e. ∛-27 = -∛27

    Therefore, ∛27 + ∛(-27) = ∛27 - ∛27 = 0

  2. Example 2: The volume of a spherical ball is 27π in3. What is the radius of this ball?

    Solution:

    Volume of the spherical ball = 27π in3
    = 4/3 × π × R3
    ⇒ R3 = 3/4 × 27
    ⇒ R = ∛(3/4 × 27) = ∛(3/4) × ∛27 = 0.90856 × 3 (∵ ∛(3/4) = 0.90856 and ∛27 = 3)
    ⇒ R = 2.72568 in3

  3. Example 3: Given the volume of a cube is 27 in3. Find the length of the side of the cube.

    Solution:

    Volume of the Cube = 27 in3 = a3
    ⇒ a3 = 27
    Cube rooting on both sides,
    ⇒ a = ∛27 in
    Since the cube root of 27 is 3, therefore, the length of the side of the cube is 3 in.

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FAQs on Cube Root of 27

What is the Value of the Cube Root of 27?

We can express 27 as 3 × 3 × 3 i.e. ∛27 = ∛(3 × 3 × 3) = 3. Therefore, the value of the cube root of 27 is 3.

If the Cube Root of 27 is 3, Find the Value of ∛0.027.

Let us represent ∛0.027 in p/q form i.e. ∛(27/1000) = 3/10 = 0.3. Hence, the value of ∛0.027 = 0.3.

Why is the value of the Cube Root of 27 Rational?

The value of the cube root of 27 can be expressed in the form of p/q i.e. = 3/1, where q ≠ 0. Therefore, the ∛27 is rational.

Is 27 a Perfect Cube?

The number 27 on prime factorization gives 3 × 3 × 3. On combining the prime factors in groups of 3 gives 3. So, the cube root of 27 = ∛(3 × 3 × 3) = 3 (perfect cube).

What is the Value of 2 Plus 8 Cube Root 27?

The value of ∛27 is 3. So, 2 + 8 × ∛27 = 2 + 8 × 3 = 26. Hence, the value of 2 plus 8 cube root 27 is 26.

What is the Cube of the Cube Root of 27?

The cube of the cube root of 27 is the number 27 itself i.e. (∛27)3 = (271/3)3 = 27.

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