 Welcome friends to another session on certs and in this session we are going to understand what are compound certs So you would have encountered certs like 2 root 2 Minus 3 root 5 now. This is not a single cert. This is a combination of two certs separated by a Negative sign so hence how do we define compound certs? So compound certs are expressions expressions Compound certs are what expressions and they are consisting of consisting of consisting of two or two or more Serds, okay, two or more Serds So it could be root 2 minus 2 3 root 5 plus 7 like that. Okay, right and then they must be connected They must be connected by connected by either plus or minus Signs, okay, so these are this is how we define a compound search. So let us say let us take some examples So examples would be we have already shown you one so three root five Plus five root three is another example. See they may be of the same order. They may not be of the same order Okay, so let us say third root of five Minus two times Seventh root of six. This is also a compound. So all our compound search mind you three root five into Five root three is not a compound. So it is not a compound. So why because it can be reducing reduced to a Not a compound So let me write this and I'm saying this could be reduced to a single sir, how you can Multiply three times five. So this can be written as three times five and root five times root three, isn't it? So which is nothing but 15 times root of five into three, which is nothing but 15 15 Okay, so hence this is when there is a multiplication or division sign then we don't consider them to be a compound search So what are compound search expressions? Obviously Consisting of two or more certs. So hence don't think that okay only two certs should be there So there is three root three minus four root two plus six root seven. This is these are all Compound certs, okay, and you have to just take care that they must be separate by plus or minus signs then you will get Compound certs now We are interested in operations of compound certs. So for example, I'm interested in multiplying two compound certs So let us say example multiply Multiply let us say root two plus root seven and With multiply this with let us say root two Minus root seven if you see both are compound certs, right now how to multiply so we will we will use all the basics of algebra To you to multiply, right? So we will treat as if this is X and this is why again, this is X and this is why So hence if you see it is nothing like X plus Y times X minus Isn't it so hence finally, you know this a minus B a plus B is nothing but X square minus Y square. So similarly what we can write here is as root two Squire minus root seven Squired so which is nothing but two minus seven, which is equal to negative five. So we use rules of algebra To operate on compound certs, let's take another example find the find the square of the question is find the square of Root seven plus root five This is a question. So basically you have to find out root seven plus root five Squire so if you see this looks like again a and this looks like B So you have to basically find a plus B whole Squired which you know by the knowledge of your identities algebraic identity is nothing but a square plus twice a B plus B square, right? So hence hit this will be root seven square plus two root seven Times root five plus root five Squired which is nothing but seven plus two root thirty five because you can multiply the numbers under the same route and This is nothing but five. So hence it is twelve plus two Thirty five. This is how we operate on compound shirts. Let's take another example where there is a Variable instead of a constant. So let us say I have to square square root of 3a plus x Plus root of 3a minus x Okay, so we have to square this ugly-looking term. Don't worry. You'll be able to do it very simply So 3a plus x plus 3a Minus x whole square, you have to write, isn't it? So again, if you see it is a plus Consider this to be a consider this to be B Then it simply becomes a plus B whole square. So hence we can write root 3a plus x squared that is a square plus two times 3a plus x times 3a minus x Right a B. So if you see this is a Square, this is 2. This is a this is B and finally I have to write this as root of 3a minus x squared Okay, so what will you get you will get? 3a plus x then Plus Two times since the roots are same so I can take both the quantities inside 3a plus x 3a minus x plus This becomes 3a minus x Right because the roots will go because there were square terms Now if you see closely this x and this minus x will just disappear and 3a plus 3a will become 6a So 6a plus Two times Under root now this if you see inside the under root there is a plus B a minus B form So I can write this as 3a Square minus x squared is it look closely. This is nothing, but if you see I'm writing it separately so that you can understand 3a plus x 3a minus x Let us say this is a If you see this one is a here and this one is B here Isn't it so it is like a plus B into a minus B so and hence it is nothing but a square minus B square, right? So what is our final thing? So this is 6a plus 2 3a square is nothing but 9a square minus x square So this is what the final answer would be so what is the learning learning is compound serves what are compound serves two serves or more serves separated by plus and minus sign and then we use the common algebraic laws and Principles to do operations on compound serves