Converting a Radical n√(a+n√b) into the Expression n√x + n√y when n=3,4,5,6, and 7

This research delves into various ways of converting a radical of the form + into the sum of two radicals .The contents derive from the well-established conversion of rearranging the nested radical + into the form (+2-)) 2 + , which works as a denesting process being that 2 - is a rational number.The motivation for this research was the intrinsic curiosity of wondering whether it would be possible to apply this expression for higher levels of power.We split the nested radical + into the sum of two radicals + by solving for and in terms of and for values of 3, 4, 5, 6, and 7.However, as the values of greater than 7 require the use of polynomial formulae greater than the cubic; we could not proceed further as it became too complex.