How to simplify SURD with fractions.

Hello everybody, welcome to my channel. So we are asked to simplify this, okay? Simplify 2 root 2. minus 3 over root 2 plus 1 over root 8 okay this is just like asking you to solve a normal the way You solve it the same way as normal fractions: addition and subtraction of fractions is done in the same way you do with regular fractions. We are going to solve this, but first of all, we need to simplify this square root of 8. You know that this square root see what I mean when you want to simplify this square root of 8? Now, okay, you're going to look for two numbers—that's when you multiply those two numbers, one of them is going to be going to be a perfect square and the other one is going to be an ordinary number, for example when You look at root 8; it can be expressed as 4 times 2, right? Root 4 times 2, then you can separate it. root 4 times root 2, okay. Now, what is root 4? Root 4 is 2, so this is the same thing as 2 times √2 is the same as 2 times √2, which equals 2√2, so that means that someone You can replace √8 with 2√2, as this is its simplest form. Okay, so when I do it Let's all solve this first of all: this is what 2 root 2 minus 3 over root 2. Okay, plus 1 over remember what I told you—this same thing as root 4 times 2, okay? So this is equal to 2 root 2 minus 1 minus 3 over root 2 plus 1 over root 4 is what 2 root 2 okay i believe You understood what I did here; now this is what we are going to solve—we are going to look at this. What is the LCM of 1 root 2 and 2 root 2? Obviously, the answer is 2 root 2 because it is simply 2 root 2. that 1 can divide root 2, can divide, and 2 root 2 can divide it as well, so we are going to draw a line your LCM is what 2 root 2 now 1 divide 2 root 2 we are going to have 2 root 2 so we are Going to use the 2 root 2 that you got as your answer to also multiply this root 2 on top here 2 root 2, just like the way you do with your normal fractions, okay, just like the way you do with your normal fractions minus root 2 divided by 2 root 2, which is 2 root 2 divided by root 2 you notice that through 2 we cancel root 2, we are left with 2, okay, so the answer you got which is 2, you are going to use it to multiply what this 3 here, all right? Plus 2 root 2 divided by 2 root 2, we still give you 1, see 2 root 2 all over 2 root 2, this we cancel, this you have what 1 Do you understand? So for this one, you're going to have 1; for this one, you're going to have 1 times this one. 1 times what is 1? Okay, I believe that you are following me, right? So we have 2 root 2 times. 2 root 2, I want to bring something home if you have something like root 2 times root 2 You know, it's the same thing as root 2 squared, right? Now, what is root 2? You know that root 2? the power of half; if you want to remove the root sign, it's like saying 2 raised to the power of half raised to the power of 2, again you notice that this 2 we cancel this 2 you have 2 raised to the power of 1 your answer is what 2 so what is what does this mean this means that when you have like 2 root 3 times root 3 you are going to have 3 root 5 times root 5 you are going to have 5, so what this means is that if you have root 3 times root 3, you are going to have 3; if you have root 5 times root 5, you're going to have 5, and so on and so forth, okay now Let us bring this to this place now so when you have 2 root 2 times 2 root 2, 2 root 2 into 2 root You are going to multiply number by number, then root by root. Okay, 2 times 2 gives us 4. Root 2 times root 2 gives us 2. Remember what I just told you, so that is what I'm going to do. Write here what I wrote, as clearly as you can see it and understand what I am about to do. So we are going to have 2 times 2 here; you are going to have 4 times root 2 times root 2. We are going to have 2; we are through with this minus 2 times 3, which gives us what—6? Okay, plus. 1 times 1 gives us 1 all over 2 root 2; now this is equal to 4 times 2 is 8 minus 6 plus 1. All over 2 root 2, okay, this is equal to 8 minus 6, we give us 2. 2 plus 1 will give us what? 3. All. over 2 root 2, okay, we're still coming to complete this—if this is the first time you're coming Okay, then help me comment in the comment section; let me know what you actually feel. about what I'm doing, thank you very much. All right, now looking at this, you're going to have Notice that there is a √2 under the bracket or as a denominator for this to be balanced, okay. You don't need this √2 here; you need an ordinary number here, so you need to eliminate this √2. and that is called rationalization; for you to rationalize it, you are going to multiply the numerator and denominator with what this your root 2, so to rationalize it we are going to have 3 over 2 root 2 times root 2 over root 2, so this is equal to 3 times root 2, which gives us 3 root 2. All over 2 is multiplying; well, you know, there's an invisible one here, 1 root 2, so it's more or less like saying 2 times 1 will give you what 2 you have 2 then root 2 times root 2 is going to gives us what root 2 times root 2 will give us what another 2 so it means that your final answer Now it becomes 3 root 2 over 2. All right, have a lovely day and bye.