Cube Root of -343

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, ∛-343 is written as (-343)^(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 -343, then y^3 can be -343. The cube root of -343 is -7, as (-7) × (-7) × (-7) = -343.

Finding the cube root of a number involves identifying the number that must be multiplied three times to result in the target number. Now, we will go through the different ways to find the cube root of -343. 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 such as -343, the prime factorization method is straightforward and effective.

Let's find the cube root of -343 using the prime factorization method: 1. Prime factorize -343: The prime factors of 343 are 7 × 7 × 7 = 343, and because it is negative, we have -1 as well. 2. Group the factors into triples: (-1) × (7 × 7 × 7). 3. The cube root is the single factor from each group: ∛-343 = -7. Therefore, the cube root of -343 is -7.

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 if it is the product of multiplying a number three times by itself. For example, (-7) × (-7) × (-7) = -343, so -343 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 denoting the cube root. Radical sign: The symbol used to represent a root, expressed as ∛. Rational number: A number that can be expressed as a fraction. The cube root of -343 is rational because it is -7.