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8.2 Simplifying, Multiplying and Dividing Radicals

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hello how are you guys what am I to do with this how to break them up into factors of perfect squares that with radicals of the same index denominator so let's get into this video taken from you for this video as well when I write anything down and you should be taking notes we would in class if your notes are not an accurate tool it's going to be very hard to help yourself on this island so you have to make sure that you're writing down everything that I do square root 13 times square root of 2 these are both radicals of the same Index this is the square root of the square root so I am allowed to multiply weather right now I can write and I can say 13 * 2 underneath one nautical 13 * 26 one more for good measure I just went down to the cube root of 2 y cube root and a cube root so I am allowed to do this I'm allowed to write one big cube root and multiply both of these inside 5 x squared x to y and now I was just remember for multiplying monomials simplify the cube root of and I can't do anything with x squared + y I just have to write them again in that cube root is my answer the cube root of x squared y let's talk about simplifying 48 factors of perfect squares I really don't get to do much with the square root of 48 that really can't be tamed V unless I see a perfect square times something else so 48 is not a perfect square however 16 is great for you guys is the square root of 16 times the square root of 3 16 * 3 is 48 and now you can see I've taken out a perfect something else that is a perfect square variable show me break that up as accident 4th is X to the fifth and again I know this is going to simplify to something when I first simplify radical we talked about yesterday how you can take the and / the route so 4/2 that can become weary and now I'm left with two things I cannot simplify the square root of 3 I can't do anything with that square roots answer Google remember your calculator for you and if you do the square root of 48 it will give you four radical free it would give you the fact that this became the floor and the radical 3 can it be simplified parts for you however you're going to have to be for your variable I had the cube root 100 ziti the night I'm not really looking for perfect squares perfect cubes because I'm dealing with a cube root beer so what I can bring 27 of 27 hi cube root of 4 because 27 * 4 is 108 I'm going to break this why did the 6th time cube root of Y squared times the cube root of 0 here's why this makes sense to break up variables in this way when you are breaking your variables up in two perfect cubes or perfect squares you need to pick numbers that are divisible by your route so I took a break it out this why to the again that were divisible by 3 because I was dividing by my root 2 and 4/8 divisible by 2 so that's why that wouldn't work but numbers are divisible by 3 no they have everything I know that the cube root of 27 can you get me 3 and now that I've written that out I'm going to crash out and lastly I know the cube root of the night organized all those three out so I know the only thing I have left under a cube root are for and why you can write that my cube root here squares and I am done sometimes we're going to have to multiply and then simplify problem we were told to simplify and we had the square root of 8X squared time well what I recommend I recommend 96 now you take this and you still in the way that we just had in the previous examples radical 16 times radical 6 because 16 * 6 + 96 + to take the Number 96 and just start dividing it by perfect square 16 by 25 the biggest one that fits in there SQ in to square root of x squared times x equal sign as well now I'm going to simplify each piece and I'll ideal going to cross that what I said besides I know the square root of squared is going to become y square root of 6 and I'm done play the best of my papers around thank you for your patience there when things don't start out very easy when things aren't say we have a problem square root -1 square root 3 to the 4th when were multiple group like terms and most of those two together separately as well I'm trying to go free ride to the fort one big root why do the four I know that radical 24 to be broken up as a square root of 4 which my perfect square can't do anything with Korea why did the force is also a perfect square snow breakdown no but I have everything can't do anything with the radical 6 can't do anything with black but remember that's 4 / the index to 4 divided by 2 squared underneath the radical right -7 times and now I am strategy there you're like factors for Skype and then hear you're having a hard time or you remember if I did do square root 24 of already 06 answer for us what you want to be able let's talk about we have a question looks like they say it was Radical 125 over radical 5 the first thing you should do whenever you have a radical or this is a property allowed if you have a radical over radical you are allowed to make it one radical distraction now inside your 125/5 can actually be simplify 125 / I still have the square root but now I have 25 in there and we see where this is going should I be there was created one radical when I had two separate that's important let's do one more of that let's say I started radical 128 / radical for once again my first set is one big radical I take care of my division 128/4 gets me 32 so I have radical 32 simplified it takes care of yourself the answer is radical 16 times radical 2 is when I can break that a bath square root of 16 is going to get me for and then I still have my radical 2 on the outside and I'm done with that the denominator I had the title rationalizing denominator example forgiving a radical 15 x squared over a radical why do the search you should make one in radical and one fraction on the inside and there we have it polynomials and Awkward over my ex I crossed one out and I must with One X on top can't really do anything yq on bottom now what we have here is a problem in algebra what we have here is a radical with a denominator and we that we can't ever have a day situation going on the radical in the bottom is I have really a radical y cubed here so I'm going to Amazon on the bottom now I'm going to have why because 3 + 3 6 and I'm a top I'm going to have y to the Third and now I'm going to take care of a few things how to reverse the square root of Y to the 6th so we can see pretty clearly on the bottom but that can be simplified now if I take this I take my power / my index to 6/2 and I get why third on the bottom I can try to break this radical up so I can simplify it radical I can break that up as y squared x y what I can do now is the square root of Y squared with gets me just watch Oliver take a look at that for a second and I see there's one more thing I can simplify now and three wise on bottom which means if I crossed went out I had two left on the bottom I have y squared left on the bottom you answer all over y squared and I'm done what do one more type of example I was rationalizing the denominator and then I'll leave you alone to simplify 3 + radical 11 all over radical 6 I want you 3 * we multiply Hugh X by radical 6 Ronco Six times radical 36 a radical number phone number for radical that was underneath it radical 6 times radical 3 + radical 6 times radical and I'll probably break plus radical 66 where is going to be 9 of course you still have it where's my video for you guys I do want to refer you to 62 is more example there are different if you want to see another one

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8.2 Simplifying, Multiplying and Dividing Radicals

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