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Cube Root of 125

The value of the cube root of 125 is 5. It is the real solution of the equation x3 = 125. The cube root of 125 is expressed as ∛125 in radical form and as (125)⅓ or (125)0.33 in the exponent form. As the cube root of 125 is a whole number, 125 is a perfect cube.

  • Cube root of 125: 5
  • Cube root of 125 in exponential form: (125)⅓
  • Cube root of 125 in radical form: ∛125

Cube Root of 125

1. What is the Cube Root of 125?
2. How to Calculate the Cube Root of 125?
3. Is the Cube Root of 125 Irrational?
4. FAQs on Cube Root of 125

What is the Cube Root of 125?

The cube root of 125 is the number which when multiplied by itself three times gives the product as 125. Since 125 can be expressed as 5 × 5 × 5. Therefore, the cube root of 125 = ∛(5 × 5 × 5) = 5.

How to Calculate the Value of the Cube Root of 125?

Cube Root of 125 by Prime Factorization

  • Prime factorization of 125 is 5 × 5 × 5
  • Simplifying the above expression: 53

Therefore, the cube root of 125 by prime factorization is (5 × 5 × 5)1/3 = 5.

Is the Cube Root of 125 Irrational?

No, because ∛125 = ∛(5 × 5 × 5) can be expressed in the form of p/q i.e. 5/1. Therefore, the value of the cube root of 125 is an integer (rational).

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Cube Root of 125 Solved Examples

  1. Example 1: What is the value of ∛125 + ∛(-125)?

    Solution:

    The cube root of -125 is equal to the negative of the cube root of 125.
    i.e. ∛-125 = -∛125

    Therefore, ∛125 + ∛(-125) = ∛125 - ∛125 = 0

  2. Example 2: Given the volume of a cube is 125 in3. Find the length of the side of the cube.

    Solution:

    Volume of the Cube = 125 in3 = a3
    ⇒ a3 = 125
    Cube rooting on both sides,
    ⇒ a = ∛125 in
    Since the cube root of 125 is 5, therefore, the length of the side of the cube is 5 in.

  3. Example 3: Find the real root of the equation x3 − 125 = 0.

    Solution:

    x3 − 125 = 0 i.e. x3 = 125
    Solving for x gives us,
    x = ∛125, x = ∛125 × (-1 + √3i))/2 and x = ∛125 × (-1 - √3i))/2
    where i is called the imaginary unit and is equal to √-1.
    Ignoring imaginary roots,
    x = ∛125
    Therefore, the real root of the equation x3 − 125 = 0 is for x = ∛125 = 5.

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FAQs on Cube Root of 125

What is the Value of the Cube Root of 125?

We can express 125 as 5 × 5 × 5 i.e. ∛125 = ∛(5 × 5 × 5) = 5. Therefore, the value of the cube root of 125 is 5.

If the Cube Root of 125 is 5, Find the Value of ∛0.125.

Let us represent ∛0.125 in p/q form i.e. ∛(125/1000) = 5/10 = 0.5. Hence, the value of ∛0.125 = 0.5.

What is the Cube Root of -125?

The cube root of -125 is equal to the negative of the cube root of 125. Therefore, ∛-125 = -(∛125) = -(5) = -5.

What is the Cube of the Cube Root of 125?

The cube of the cube root of 125 is the number 125 itself i.e. (∛125)3 = (1251/3)3 = 125.

Is 125 a Perfect Cube?

The number 125 on prime factorization gives 5 × 5 × 5. On combining the prime factors in groups of 3 gives 5. So, the cube root of 125 = ∛(5 × 5 × 5) = 5 (perfect cube).

What is the Value of 16 Plus 2 Cube Root 125?

The value of ∛125 is 5. So, 16 + 2 × ∛125 = 16 + 2 × 5 = 26. Hence, the value of 16 plus 2 cube root 125 is 26.

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