 hello friends so in this session we are going to understand how to compare two certs of different order so if you remember these there are you know what is the what is meant by order of a cert so what nth root a particular number is that nth thing is called the order for example third root of five so hence this third is of third order isn't it our cubic third it is third order second similarly second root of let's say seven this is second order second order third you learned this in the previous session now the question is how do we compare two certs two given certs now if someone asks which is greater second root of three or third root of two so how to solve such questions and basically how to understand which one is more or which one is less so for that what you need to do is first first thing is to convert them into the same order so we have learned how to convert them into the same order so the order here is two order here is three so we have to convert both of them into same order now once the order is same then you can compare the two certs how let us see so how do we make them of the same order so we have to find out lcm of two and three yeah which is nothing but six so let us convert both of them into order of six so square root of three can be written like this and then we learned how to convert this into order six how to do that one by two into three by three you do so what will you get you will get three to the power three upon six isn't it so this is sixth root of three cubed correct which is equal to sixth root of 27 okay now second case is third root of two right which is nothing but two to the power one by three which can be written as two one by three times two by two so hence it is two to the power two by six which is nothing but sixth root of two square right which is sixth root of four now both the orders are same now once the order are same then you can compare just as you compare any two given numbers now clearly 27 is greater than four right that means if I raise both to the power one by six this will be the case remember when you are raising two numbers to the positive power the inequality doesn't change right so now what will happen so hence what what do I understand I understand sixth root of 27 is now in greater than sixth root of four correct so hence so hence sixth root of 27 is greater than sixth root of four so equivalently sixth root of 27 was nothing but square root of three is greater than third root of two that's what the conclusion is