Cube Root of 125/216

We have learned the definition of the cube root. Now, let’s learn how it is represented using a symbol and exponent. The symbol we use to express the cube root is the radical sign (∛), and the exponent we use is ⅓.

In exponential form, ∛(125/216) is written as (125/216)^(1/3). The cube root is just the opposite operation of finding the cube of a number. For example: Assume ‘y’ as the cube root of 125/216, then y³ can be 125/216. Since 125 and 216 are both perfect cubes, we can express the cube root of 125/216 as (∛125)/(∛216), which simplifies to 5/6.

Finding the cube root of a number is to identify the number that must be multiplied three times resulting in the target number. Now, we will go through the different ways to find the cube root of 125/216. The common methods we follow to find the cube root are given below:

• Prime factorization method
• Simplification method

Since 125/216 is a fraction made of perfect cubes, we can use the simplification method to find its cube root.

Let's find the cube root of 125/216 using the simplification method.

The formula is ∛(a/b) = (∛a)/(∛b) where: a = the numerator b = the denominator

Substituting, a = 125; b = 216 ∛(125/216)

= (∛125)/(∛216)

Since 125 = 5³ and 216 = 6³, we find:

∛125 = 5 and ∛216 = 6

Thus, ∛(125/216) = 5/6

The cube root of 125/216 is 5/6.

• Cube root: The number that is multiplied three times by itself to get the given number is the cube root of that number.
   
• Perfect cube: A number is a perfect cube when it is the product of multiplying a number three times by itself, resulting in a whole number. For example, 5 × 5 × 5 = 125, therefore, 125 is a perfect cube.
   
• Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In the context of cube roots, ⅓ is the exponent indicating the cube root of a number.
   
• Radical sign: The symbol used to represent a root, expressed as (∛).
   
• Rational number: The numbers that can be expressed as the quotient of two integers are rational. For example, the cube root of 125/216 is rational because it simplifies to 5/6.