Cube Root of 27/64

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, ∛(27/64) is written as (27/64)^(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 27/64, then y³ can be 27/64. Since 27/64 is a perfect cube, its cube root is exactly 3/4.

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 27/64. The common methods we follow to find the cube root are given below:

• Prime factorization method
• Exact calculation method

Using the properties of fractions Since 27/64 is a perfect cube, we can find its cube root exactly by either using the cube root of the numerator and the denominator separately or using properties of fractions.

Let's find the cube root of 27/64 using exact calculation:

The cube root of a fraction is the cube root of the numerator divided by the cube root of the denominator.

∛(27/64) = ∛27 / ∛64 ∛27 = 3 (Since 3³ = 27 ∛64 = 4 and 4³ = 64)

Therefore, ∛(27/64) = 3/4

The cube root of 27/64 is exactly 3/4.

• 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. For example, 3 × 3 × 3 = 27, and 4 × 4 × 4 = 64, so 27/64 is a perfect cube.
   
• Fraction: A part of a whole, represented as a/b where a is the numerator and b is the denominator.
   
• Rational number: A number that can be expressed as a fraction a/b, where a and b are integers and b is not zero.
   
• Radical sign: The symbol used to represent a root, expressed as (∛).