Cube Root of 819

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, ∛819 is written as 819^(1/3). The cube root is the inverse operation of finding the cube of a number. For example, assume 'y' as the cube root of 819, then y³ can be 819. Since the cube root of 819 is not an exact whole number, we can write it as approximately 9.343.

Finding the cube root of a number involves identifying the number that, when multiplied by itself three times, results in the target number. Various methods can be used to find the cube root of 819:

• Prime factorization method 
• Approximation method 
• Subtraction method
• Halley’s method

To find the cube root of a non-perfect cube number like 819, Halley’s method is often used.

Let's find the cube root of 819 using Halley’s method.

The formula is: ∛a ≅ x((x³ + 2a) / (2x³ + a)),

where: a = the number for which the cube root is being calculated

x = the nearest perfect cube

Substituting, a = 819;

x = 9

∛a ≅ 9((9³ + 2 × 819) / (2 × 9³ + 819))

∛819 ≅ 9((729 + 2 × 819) / (2 × 729 + 819))

∛819 ≅ 9.343

The cube root of 819 is approximately 9.343.

• 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, 2 × 2 × 2 = 8, therefore, 8 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 used to represent a root, expressed as (∛).

• Irrational number: Numbers that cannot be expressed as a simple fraction are irrational. For example, the cube root of 819 is irrational because its decimal form goes on continuously without repeating the numbers.