5 to the Power of What Equals 125

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

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).

☛ Also Check:

• Cube Root of 4000
• Cube Root of 21
• Cube Root of 1729
• Cube Root of 5
• Cube Root of 52
• Cube Root of 65
• Cube Root of 70

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 = (125^1/3)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.

5 to the Power of What Equals 125

Source: https://www.cuemath.com/algebra/cube-root-of-125/

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