A simplification of radical question.

This is actually interesting; let's do it together. We are asked to simplify 2 root 2. minus 3 root 2 plus 1 over root 8 okay our solution solution let me stay this side so First of all, we have what 2 root 2, okay, minus 3 over root 2. plus 1 over now this root 8, let's put it in its simplest form. We know we can express root 8 as What is root 4 times 2? Yes, now let's go ahead and solve. So this expression: 2 root 2 divided by 1. minus 3 over root 2 plus 1 over we all know that you can split this, right? Yes, according to the The rule for this is that you can split it as root 4 times root 2, okay? Now let's continue from this point. We can write this as 2 root 2 over 1 minus 3 over root 2, okay? So this particular one, now we have plus 1 over now what is root 4? square root of 4 is 2, so we have 2 times root 2 is the same thing As 2 root 2, so this is what we have now at this point. What is the LCM of 1 root 2 and 2 root 2? The answer is 2 root 2, so let's express them using the same terms so that they have the same form. denominator, which is going to be their LCM. Now, when 2 root 2 is divided by 1, you are going to You have 2 root 2, right? So you still have 2 root 2, so it's going to multiply by 2 root 2, all right. Minus now, when 2 root 2 is divided by root 2, you'll have 2 remaining, so that's 2 times 3. Okay, so we are going to have 2 times 3, all right, plus now this 2 root 2, we also divide 2 root 2. to give us 1, so we are going to have that one; we got multiplied by what this one, okay, so this is equal to now 2 root 2 times 2 root 2, 2 root 2 times 2 root 2, this is what we have here, 2 root 2 times 2 root 2; now your number will multiply your number, okay? So 2 times 2 is going to give US 4 if you've watched this far, then I think it's and this is the first time you're Coming across this channel, I think it's time for you to click that subscribe button. and also don't forget to comment, like, and share on your notification bell as well is the only way you're going to show me or express to me how you feel about my channel All right, okay, now 2 times 2 gives us 4, then the square root: we multiply square root by square root; root 2 times root 2 we give us 2 root 2 times root 2 we give us 2 this is it square root of 2 times square root of 2 can be written as the square root of 2 times 2, which is the same as the square root of 4. which is the same thing as 2, so the square root of 2 times the square root of 2 gives us 2 That means when we multiply 2 root 2 by 2 root 2, we are going to get 4 times 2 and 4. times 2 gives us what 8, all right, but I'm not going to skip it much at this stage, so we are going to solve it twice 2 gives us 4 times root 2 times root 2 we get 2 okay all right let's Now 2 times 3 gives us 6, plus 1 times 1 gives us 1, everything divided by 2 root 2 all. Alright, let's continue now this is equal to 4 times 2, which gives us 8 minus 6 plus 1 divided by 2 root 2, remember there is something called rationalization, so we are not going to, we are We're still working on this because you need to eliminate this square root of 2, so you'll have to stay put. And see the final solution, yes. So let's solve now. Now we have, um, 8 minus 6, which gives us 2. and 2 plus 1 gives us 3, okay, so you now have 3 divided by what—2 root 2? 3 divided by 2 root 2. But as I said, in mathematics, it's not correct for you to write "to have a third" as your word. since your denominator is incorrect, to rationalize the denominator we are going to multiply the multiply both the numerator and the denominator by root 2, since root 2 is what we want to eliminate, right? So we you are going to multiply the numerator and the denominator by root 2, all right, now this is It is going to be equal to 3 times the square root of 2; we get 3 root 2 over 2 root 2 times root 2, remember that. √2 is the same thing as 1√2, but it's just not standard to write 1√2. Rather than writing just root 2, why are you multiplying this and this as usual? You know how we did it. Now 2 is going to multiply 1 to give us 2; times root 2 is going to multiply root 2 to give us Another 2, okay, so this gives us 3 root 2 over 4, and this is the final solution. Thank you so much for watching, and have a great day! Bye.