Cube Root of -2197

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, ∛(-2197) is written as (-2197)^(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 -2197, then y^3 can be -2197. Since -2197 is a perfect cube, the cube root of -2197 is exactly -13.

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 -2197. 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 -2197, the prime factorization method is straightforward and effective.

Let's find the cube root of -2197 using the prime factorization method. Firstly, we find the prime factors of 2197: 2197 = 13 × 13 × 13 Since -2197 is negative, its cube root will also be negative. Therefore, the cube root of -2197 is -13.

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, 13 × 13 × 13 = 2197, therefore, 2197 is a perfect cube. Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In ∛(-2197), ⅓ is the exponent which denotes the cube root of -2197. Radical sign: The symbol that is used to represent a root, expressed as ∛. Rational number: A number that can be expressed as the quotient or fraction of two integers. The cube root of -2197 is rational because it equals -13.