Cubed Square Root Of 125

Cube Root of 125

The value of the cube root of 125 is v. It is the real solution of the equation x³ = 125. The cube root of 125 is expressed every bit ∛125 in radical form and every bit (125)^⅓ or (125)^0.33 in the exponent form. Every bit 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

What is the Cube Root of 125?

The cube root of 125 is the number which when multiplied past itself 3 times gives the product every bit 125. Since 125 tin be expressed as five × v × 5. Therefore, the cube root of 125 = ∛(5 × 5 × five) = five.

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

Cube Root of 125 by Prime Factorization

Prime factorization of 125 is 5 × five × 5
Simplifying the above expression: 5ⁱⁱⁱ

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

Is the Cube Root of 125 Irrational?

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

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Cube Root of 125 Solved Examples

Example i: 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.due east. ∛-125 = -∛125

Therefore, ∛125 + ∛(-125) = ∛125 - ∛125 = 0
Instance two: 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
⇒ aⁱⁱⁱ = 125
Cube rooting on both sides,
⇒ a = ∛125 in
Since the cube root of 125 is v, therefore, the length of the side of the cube is 5 in.
Example three: Find the real root of the equation 10³ − 125 = 0.

Solution:

x³ − 125 = 0 i.east. x³ = 125
Solving for ten gives us,
x = ∛125, x = ∛125 × (-1 + √3i))/2 and ten = ∛125 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
ten = ∛125
Therefore, the existent root of the equation x^three − 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 tin limited 125 as 5 × five × v i.e. ∛125 = ∛(5 × 5 × 5) = five. Therefore, the value of the cube root of 125 is 5.

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

Permit the states represent ∛0.125 in p/q form i.e. ∛(125/1000) = 5/ten = 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) = -(five) = -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.due east. (∛125)^three = (125^1/3)ⁱⁱⁱ = 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. And so, the cube root of 125 = ∛(five × 5 × 5) = 5 (perfect cube).

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

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