Cube Root of 314432

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, ∛314432 is written as 314432^(1/3). The cube root is just the opposite operation of finding the cube of a number. Since 314432 is a perfect cube, its cube root is an exact whole number, which is 68.

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 314432. The common methods we follow to find the cube root are given below:

• Prime factorization method
• Halley’s method

Since 314432 is a perfect cube, we can use the prime factorization method to find its cube root.

Let's find the cube root of 314432 using the prime factorization method.

First, find the prime factors of 314432: 314432 = 2^8 × 7^3

To find the cube root, take the cube root of the prime factors:

∛314432 = ∛(2⁸ × 7³) = 2^(8/3) × 7^(3/3) = 2² × 7¹ = 4 × 7 = 28

Thus, the cube root of 314432 is 68.

• 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, 68 × 68 × 68 = 314432, therefore, 314432 is a perfect cube.

• Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 314432^(1/3), ⅓ is the exponent which denotes the cube root of 314432.

• Radical sign: The symbol that is used to represent a root is expressed as (∛).

• Rational number: A number is rational if it can be expressed as a fraction or a whole number. The cube root of 314432 is rational because it equals 68, a whole number.