Cube Root of -2744

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, ∛-2744 is written as (-2744)^(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 -2744, then y³ can be -2744. Since the cube root of -2744 is an exact value, we can write it as -14.

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 -2744. 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 -2744, we can use the prime factorization method.

Let's find the cube root of -2744 using the prime factorization method. First, we factorize -2744: -2744 = -2 × 2 × 2 × 7 × 7 × 7. Since we have three 2s and three 7s, we can group them as: (-2 × 7) × (2 × 7) × (2 × 7) = (-14) × 14 × 14. Therefore, the cube root of -2744 is -14.

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, (-14) × (-14) × (-14) = -2744, therefore, -2744 is a perfect cube. Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In (-2744)^(1/3), ⅓ is the exponent which denotes the cube root of -2744. 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 a whole number. The cube root of -2744 is rational because it is -14.