How to simplify surds, addition and subtraction of similar surds.

Yeah, welcome to my channel. Let's get straight to the point. Okay, we are asked to simplify. 3√2 − √32 + √50 + √98 to simplify, you need to factor that number into two parts, one of which will be a perfect square, the other will be an ordinary number now first of all what is a perfect square a perfect square is that number that you can get its square root without the square root having a decimal, for example 25 is a perfect square; that's why if you say the square root of 25, you get 5—it's not a decimal. It's a whole number now. For example, again, the square root of 9 is 3, so it means that 9 is a perfect square. 25 is also a perfect square, so when you're asked to simplify the square root, you're going to put that square root. into a perfect square and an ordinary number. Now let's do that. The question says we should simplify: 3√2 − √32 + √50 + √98; now, 3√2 is already in its Simplest form, so we are going to write it again: 3 root 2, this is equal to minus; this is our problem. This square root of 32 is not in its simplest form, okay? So how do we now simplify it? Looking at this number. This 32, how do we get the two numbers that we are going to use to simplify it? You are going to write. You're 32 and you're going to draw your line; I'm just giving you the simplest way you can do it. so that you understand, so that you will get your answer right, this takes Two; now the simplest number that can divide it, the smallest number that can divide it, is two. Okay, so if we divide two by three, we're going to have one with a remainder of one. 12 you're going to have what six now I'm going to stop here why because I've gotten a perfect Square whether the perfect square is here or here; I've gotten a perfect square, I'll stop because This means that 2 times 16 will give me 32, so I'm now going to rewrite this root 32 as root what 16 times 2, do you understand? 16 times 2. Okay, we're done with what square root of 32. Let's move on. 2 root 50. Now we are going to divide again by the smallest possible number. Now, what is the The smallest number that can divide 50 is 2, so we start with 2. If 2 divides 5, then you will have a 2 remainder 1 if we divide 10 you are going to have 5 all right if you look at this we have 2 and 25, I will stop again, why? Because I know that 25 is a perfect square, the square root of 25. It will give me 5, so that means 2 times this 25 will give me 50, so I will stop. I will now write. plus what is root 25 times 2, okay, plus we are now, what is remaining now, root 98, right, the same thing What is the smallest number that can divide 98? If 2 divides 9, you are going to have 4.4 remainder 1 if we divide 18, you are going to have 9; I will also stop here because 49 is a perfect square, okay as well. I haven't gotten a perfect square yet; I'll continue dividing until I do. Perfect square either here or here, okay. Now, 2 times 49 will give us 98, so I'm going to stop here. because the square root of 49 gives me 7, now I'm going to replace this square root of 98 with what the square root of 49 times 2 Okay, so we're done with this, so this is equal to 3 root 2 minus you split this You split them, so it's now going to be root 16 times root 2, okay? Split them all right, plus You are going to split this one toward root 25 times 2, and you're also going to split this one. towards root 7, sorry, root 49 times root 2, all this, this one has root as well, root 2 Okay, now I've split them. Okay, if you've followed me to this stage, it means that you are actually enjoying what I'm doing, so I'll advise you to subscribe at this point subscribe to this channel if you haven't done so already, and click the notification bell so that you'll be notified Whenever I upload a new video, I want you to feel my absence in my next video, okay? Alright, please also give it a thumbs up so the video can spread, so that students can benefit. Actually, see this and learn from this. All right, now when you see this, what do we do at this point? This is equal to 3 root 2 minus. Now, what is root 16? Root 16 is 4, so you now write 4 root 2 because 4 times root 2 is 4 root 2, so we have simplified this; now, 4 root 2 is the simplest form of root 32 okay all right let's go ahead now what is root 25? root 25 is 5 times root 2 is root 2 So you have 5 root 2, which means that 5 root 2 is the simplest form of root 15, all right. plus you have root 49 which is 7, which is 7, so write your 7 times root 2 means root 2, okay, at this point now there is something called similar sorts, similar sorts. Now, what are Similar sorts are those numbers that have what? Similar sorts—let me just explain. This is 3 root 2. Notice that all of them have root 2, root 2, root 2, root 2. It means that they are all similar. Do you understand? All of them are similar. because they have the same sword attached to them, so this is 3 root 2, 4 root 2, 5 root 2 7 root 2, so they are similar types. Now, how do you solve similar types? Solving similar types of problems is very easy; all you need to do is solve their words. their coefficients and you are going to write root 2 as the final answer now just see what I Mean you're going to write this 3, open your brackets, this 3 minus this 4 plus this 5 plus this 7 everything root 2 you see how easy it is 3 minus 4 plus 5 plus 7 root 2 okay now this is equal to 3 minus 4 is going to give us what minus 1, right? Minus 1 plus 5 minus 1 plus 5 now when you have something like this, it's the same as letting me bring it out so that it will not look like, so we have 3 minus 4, which gives us minus 1, so minus 1 plus 5 minus 1 plus 5 is The same thing as if you write your plus first; okay, you can decide to write this one with a positive sign. Sign first, so if I write it first, you know that plus 5 is the same thing as 5, all right? 5 minus 1. so you are going to have what you are going to have 4, so it means that minus 1 plus 5 is equal to what 5 minus 1, which will give us 4, so it means that 3 minus 4 will give us minus 1 minus 1 plus 5 will give us 6, then 4 plus 7 is going to give us 11. 4 plus 7 will give us 11. so it means that this is equal to 11 root 2, and this becomes Our final answer. Thank you for watching. See you next time. Bye.