 Hello folks, welcome again. So in the last session, we studied what are Serds and we studied how to express Serds as a Product of rational and in irrational part and vice versa Now we are going to understand one more important topic and that's called similar Serds. Okay, so what do we mean by similar Serds? Now similar Serds are two or more Serds Obviously you have to have multiple Serds to compare so that you can talk about similarity. So two or more Serds Are said to be similar when they can be reduced in such a way that they have same Irrational factors Right, so we learned how to convert a pure Serd or a complete Serd into a product of a rational and an irrational Factor so if by after reduction you see that the irrational factors are same then the Serds are called similar Example root 45 and root 80 are similar Serds Why because root 45 you can see is nothing but under root 9 into 5 which is under root 3 square into 5 Which is under root 3 square into under root 5 which is equal to 3 times under root 5 3 root 5 right so 3 root 5 is root 45. What about root 80? Root 80 is under root 16 into 5 4 under root 4 square into 5 then finally under root 4 square into Root 5 sorry I missed the root sign here and then this 4 root 5 Right now if you compare these root 45 and root 80 you will see the root 5 component is Both in the both they are same right so your rational part are same So hence we'll say 3 root 5 and 4 root 5 are similar Serds Let me take another example and explain it to you. So another example is root 27 and root 275 are similar. Why because root 27 if you reduce it You will get 3 root 3 and root 75 if you reduce you'll get 5 root 3, right? So if you see again the Irrational part in both the Serds same So hence it is similar Serd another such examples There would be so many examples minus 2 root 7 and 5 root 7 are similar Okay, then 4th root of 3 and 5 times 4th root of 3 are similar because irrational parts are same all these are similar Serds Something which is not similar for example root 5 is never similar to root 3, right? They are not similar root 20 let us say is nothing, but if you see root 20 is 2 root 5 isn't it so root 20 is not similar to root 18 which is nothing but 3 root 2 Correct. So these two are not similar. You understood what is similarity now similarity of search is very important while doing some operations And we'll see now How it impacts, right? So what is the importance of finding similarity because only similar Serds Could be added or subtracted Now dissimilar Serds or not similar Serds can be multiplied and divided but for addition and subtraction which is going to be a big thing for you Later on because most of you would be doing such mistakes later And hence to take care of it We have we are now saying that please be careful about the operations on Serds now similar Serds only can be added and subtracted Okay, they can any type of Serds can be multiplied and divided except During division you have to make sure that you're not dividing by zero But in case of addition and subtraction only similar Serds can be added. So two or more similar Serds Can be added, right? So root of 45 plus root 80 if you see is nothing but 7 root 5 5 because root 3 root 5 plus 4 root 5 you can take root 5 common So 3 plus 4 within the brackets. So 7 root 5 Right, this is this is 7 into root 5. So please do not get confused between this And 7th root of 5 guys So if you see if you see 7 written in this valley, then it is 7th root But if you see 7 written outside the root sign, it is 7 times square root of 5, right? So when the nothing is mentioned it is 2 over here. So it is 7 times square root of 5 So don't make mistakes in these cases, right? Now similarly if root 27 plus root 75 is there so root 27 is 3 root 3 root 75 is 5 root 3 we just saw above now are they similar? Yes, because their irrational parts are similar same. So hence I can add Simply as if you know, you're adding 3x plus 5x isn't it? It's it's it's like if you call root 3 as x So it's like adding 3x plus 5x Which is nothing but 8x similar similar to the algebraic relation what we have studied Okay, similarly subtraction can be done only with similar So hence again, we take the same root 80 and root 45 you subtract You'll get 4 root 5 minus 3 root 5 Which is root 5 1 root 5 that is right. So 1 is hidden over here 1 into root 5 now root of 27 Minus root of 75 is 3 root 3. We just saw above minus 5 root 3 So 3 root 3 minus 5 root 3 is minus 2 root 3, right? You can also express this as what can you express this as So you can express this as minus 2 to the power 2 whole Half right same thing into root 3. Isn't it? Or this can be written as this can be written as minus under root 4 into root 3 Isn't it? Which is nothing but minus under root 4 into 3 which is nothing but minus root 12 So you can express in whichever way you can reuse it till this level and leave it like that also now So these are what what did we learn? We learned about similar certs We learned that only similar certs could be added and subtracted for multiplication and division. There is no such restriction So please understand whenever you see a plus sign be aware only when if you see a similarity of the certs Then only you operate we also learned this that don't get confused between things like 3 root 5. This is third root 5, right? Third root 5 is different from 3 times root 5 Which is usually written as 3 and along with it root 5, right? So these two are Different quantities. So please be careful about it