Perfect Cube

The perfect cube is the result of multiplying the same integer three times. Multiplying the number 4 three times, for example, yields 64. As a result, the number 64 is a perfect cube. Perfect cube = number x number x number. If a number can be broken down into a product of the same three numbers, it is said to be a perfect cube.

Definition of a Perfect Cube

A perfect cube is the product of three identical numbers. To see if a number 'N' is a perfect cube, multiply it by itself three times and see if the result is the number 'N'. If you answered yes, you have a perfect cube. A perfect cube has the numbers 1, 8, 27, and 64 as examples. A perfect square can be made by multiplying two numbers together. It's not the same as a flawless cube. Both positive and negative integers can be used to make perfect cubes. For example, -64 is a perfect cube since it is the result of multiplying -4 three times.

Root Cube

When we say a number has been cubed, we indicate that it has been multiplied three times. The process of cubing a number is reversed with cube root. When the number 5 is cubed, for example, we obtain 5 x 5 x 5, which equals 125. The number 125 has a cube root of 5. This is because multiplying the number 5 three times yields 125. Cube root is represented by the symbol: It's the same as the square root sign, except with the addition of a '3' to indicate that it's a cube root. The cube root of an integer can be represented in exponent form as (number)1/3.

There is a method for determining whether or not larger numbers are perfect cubes. To check, add up all of the digits in the number and determine if the result is 0, 1, 8, or 9. If it's any of these, it may be a perfect cube, although that isn't always the case. To determine if it is a perfect cube, we must repeat the prime factorization procedure described before. This is a method for determining if a number is a perfect cube or not, however it is not always guaranteed.

This technique is utilized because let's assume we're given a number, like 8768, and we're not sure if it's a perfect cube or not. So, we calculate the sum of this number's digits and see if it's 0, 1, 8, or 9. If the number isn't one of these four, we don't need to factorize it to see if it's a perfect cube. In other words, if the sum is not equal to 0, 1, 8, or 9, this technique just bypasses the prime factorization procedure. In this example, the total of the digits of the integers 8768 equals 29, the sum of 2 and 9 is 11, and 1 + 1 = 2. As a result, the answer isn't 0, 1, 8, or 9. As a result, it's easy to deduce that 8768 isn't a perfect cube.