Cube Root of -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, ∛-216 is written as (-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 -216, then y^3 can be -216. The cube root of -216 is -6, because (-6) × (-6) × (-6) = -216.

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 -216. The common methods we follow to find the cube root are given below: Prime factorization method Approximation method Subtraction method Halley’s method Since -216 is a perfect cube, we can use the prime factorization method to find its exact cube root.

Let's find the cube root of -216 using the prime factorization method. The prime factorization of 216 is: 216 = 2 × 2 × 2 × 3 × 3 × 3 Therefore, -216 = -1 × 2 × 2 × 2 × 3 × 3 × 3 Grouping the factors in triples gives us: (-1 × 2 × 3) × (2 × 3) × (2 × 3) Thus, the cube root of -216 is -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. A perfect cube always results in a whole number. For example, (-6) × (-6) × (-6) = -216, therefore, -216 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), ⅓ is the exponent which denotes the cube root of a. Radical sign: The symbol that is used to represent a root, expressed as (∛). Rational number: A number that can be expressed as a fraction or ratio, where both the numerator and the denominator are integers. The cube root of -216 is rational because it is -6.