Cube Root of 0.000729

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, ∛0.000729 is written as 0.000729^(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 0.000729, then y^3 can be 0.000729. Since the cube root of 0.000729 is an exact value, we can write it as 0.09.

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 0.000729. The common methods we follow to find the cube root are given below: Prime factorization method Approximation method Subtraction method Halley’s method To find the cube root of a perfect cube number like 0.000729, we can use the prime factorization method. Since 0.000729 is a perfect cube, using prime factorization is efficient.

Let's find the cube root of 0.000729 using the prime factorization method. 0.000729 can be expressed as 729/1000000. We find the prime factors of 729, which are 3 × 3 × 3 × 3 × 3 × 3. Grouping the prime factors into triples, we have (3 × 3 × 3) × (3 × 3 × 3), which equals 27 × 27. Thus, the cube root of 729 is 9. Since we took the cube root of 1000000 as 100, the cube root of 0.000729 is 9/100 = 0.09.

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. A perfect cube always results in an exact value. For example: 0.09 × 0.09 × 0.09 = 0.000729, therefore, 0.000729 is a perfect cube. Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In a^(1/3), 1/3 is the exponent which denotes the cube root of a number. Radical sign: The symbol that is used to represent a root which is expressed as (∛). Rational number: The numbers that can be expressed as a fraction of two integers are rational. The cube root of 0.000729 is rational because it terminates and can be written as 9/100.