Analysis of the Relationship between the nth Root which is a Whole Number and the n Consecutive Odd Numbers

Abstract

The study was undertaken to establish the relationship between the roots of the perfect numbers and the nconsecutive odd numbers. Odd numbers were arranged in such a way that their sums were either equal to the perfectsquare number or equal to a cube. The findings on the patterns and relationships of the numbers showed that therewas a relationship between the roots of numbers and n consecutive odd numbers. From these relationships a generalformula was derived which can be used to determine the number of consecutive odd numbers that can add up to getthe given number and this relationship was used to define the other meaning of nth root of a given perfect numberfrom consecutive n odd numbers point of view. If the square root of 4 is 2, then it means that there are 2 consecutiveodd numbers that can add up to 4, if the cube root of 27 is 3, then there are 3 consecutive odd number that add up to27, if the fifth root of 32 is 5, then it means that there are 5 consecutive odd numbers that add up to 32.