 Hi friends, so continuing with the sessions now we are on two serves of same order. We have seen what are serves what are Similar serves and we have also solved a few problems around that now in this session We are going to study serves of same order. Okay. Now serves those serves So I will be writing what is meant by serves of same order Serves Serves are Said to be Said to be of Same order when when is that same order and what type of serves are? Serves of same order when? they have When they have All when they have got when they have got the same Root symbol Okay, so those serves will be called serves of the same order for example Root of five that is square root of five square root of three then Square root of four to the power five Square root of X to the power three all are Serves of Same order Same order and in this case order is to Order is equal to two because you are finding the square root. So order is two similarly third root of four Third root of five square third root of Y and X to the power Four by three all are Serves of Order Three okay, so this is what? Serves of same order are called the same order so the order is to then you know quadratics. These are also called quadratic Serves quadratic Serves and These are order three Serves are called cubic Serves Okay cubic Serves Now, let us understand how to reduce Serves of different orders Serves of different orders to equivalent Serves of same order Okay, so we want to reduce Serves of different order into equivalent Serves of same order. What does it mean? Let us say I have Cube root of two and let us say third root of four Now clearly this order is two here and the order of this Serves is three here. So they are not Similar neither they are of same order. No, so how to reduce them to same order Serves So what do we do? What is the root here second root of two isn't it? So hence what do we do first step is? find the LCM LCM of Two and three Two and three so which is equal to six okay now We will be reducing both the Serves to the order of Six how to do that? So clearly two to the power Root two is nothing but two to the power half Okay, so what can I do? I can write two to the power half can be represented as half into three one by three into two by three You have a two by three. Sorry. So this is what we can say About square root of two which is eventually two to the power three upon six So that means it is sixth root of eight Isn't it so that is how I can say or I can Equate two to the power half as sixth root of eight now What about third root of four third root of four is nothing but four to the power one by three Again, I'll make it sixth root. So to make it sixth root. I'll do two by six Isn't it? So hence it is nothing but sixth root of four square, which is sixth root of 16 Isn't it? So what do we observe? We observe that now both of them are of sixth order Order order six and hence now they are a same order. So it isn't it. Let's take another example Example number two. Let us say we have sixth root of three and Eighth root of two Eighth root of two now both are of different orders. What is the order here? Here the order is six and here the order is eight. So we have to Convert it into same order third. So what is LCM of so step is LCM of Six and eight What is LCM of six and eight it is 24, isn't it 24? So let us Convert both into 24th order third. So what do we do three to the power one by six is nothing, but Three to the power four by 24, isn't it? So hence it is 24th root of Three to the power four. So hence it is nothing but 24th root of 81 Correct next. What about Two to the power one upon eight is nothing but two to the power Three upon 24. Isn't it three upon 24 is one by eight. So hence I can write this as 24th root of two cube Which is equal to 24th root of Eight, right? So hence now we see both are of order Order 24 correct now I have reduced Two serves of different orders into two serves of same order This will be very very useful when you are doing mathematical calculations with surge So for to practice more you can download the worksheet and work on those problems