Cube Root of -729

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, ∛(-729) is written as (-729)^(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 -729, then y^3 can be -729. The cube root of -729 is -9 because (-9) × (-9) × (-9) = -729.

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 -729. 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 like -729, the prime factorization method is very effective.

Let's find the cube root of -729 using the prime factorization method. First, factor -729 into its prime factors: -729 = -1 × 3 × 3 × 3 × 3 × 3 × 3. We group the factors into sets of three: (-1) × (3 × 3 × 3) × (3 × 3 × 3). Each set of three identical factors gives one factor of the cube root. Thus, ∛(-729) = -3. The cube root of -729 is -9.

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, (-9) × (-9) × (-9) = -729, therefore, -729 is a perfect cube. Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In (-729)^(1/3), ⅓ is the exponent which denotes the cube root of -729. Radical sign: The symbol that is used to represent a root which is expressed as (∛). Negative cube root: A negative number that, when multiplied by itself three times, results in a negative perfect cube. For example, ∛(-729) = -9.