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I'll smell my marker.
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You know what I did?
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Got it.
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Alright, what we're going to do here is we have two radicals that we need to multiply
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together.
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So there's a couple of ways we can do this.
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First way is you could just multiply, multiply everything that's inside this radical
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time of this, since they are products and since they're both individual terms.
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We can't just multiply them and then take the root of that.
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A lot of times though this is going to give us a large number that we really don't want to deal with.
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You know, if I was dealing with something, let's say two times, let's say which one I want to do two times, let's do nine.
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Two times root of nine, well then I can multiply this and this should make sense.
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I multiply it two times nine is going to give me the square root of 18.
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Then I can reduce this down and I'll do it two different ways.
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First way I'll do the fact in a way.
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Two, nine, three times root.
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So you factor it two times nine, multiply it to give you 18.
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And so you factor this, you can't factor it two anymore.
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You factor nine to three to three.
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Since we're taking the square root, I'm going to group the two of them.
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So therefore I'll have three.
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It comes out times the square root of two.
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Since that's left over I can't take the root that out.
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However, so that's what would happen if you had, you know, you can just multiply this.
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You could multiply 18 times 14.
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I don't know what it is, I'll stop my head, but I don't really want to try to turn it, turn it at and then try to factor that out.
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That seems like too much work for me.
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So in no way that we can do this, in a no way to factor, or I'm sorry to simplify your radical,
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is I'm going to look at simplifying both of these first and then multiplying them.
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So one other way you can simplify a radical 18 is I can say what is a square number?
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Remember square numbers are four, nine, 16, 25.
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What square number evenly divides into 18?
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And I've figured out that nine evenly goes into their two times.
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So I'm going to rewrite 18 as a product of a square number times another number.
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So I can rewrite 18 as square root of nine times two times square root of 14.
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Well, the reason why this is helpful is because the products are, you know, the rules of radicals allows me to split up my two radicals.
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So since I'm doing multiplication, I can actually split up taking the root of multiple these.
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Therefore, nine times three times square root of two times square root of 14.
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Now I haven't done anything with square root of 14 because I am drinkly already know that you can't reduce the square root of 14.
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There is no number, you know, if you're in a factor in this, two seven, those are both prime numbers, as is 14's a prime number as well, or not prime number.
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But two and seven are both prime numbers, so therefore, you know, there's nothing else you can factor that for.
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So now I have three times radical two times radical 14. Well, I can multiply these two since they're both, since I'm taking the radical of both of them.
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So I have three times the square root of two times 14 is 28.
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And then again, last check, I don't see is there anything, is there any square number that divides evenly into those?
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And you could say yes, I can actually take the four divides evenly to there.
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So I can say four times four times seven.
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And I can split that up into three times radical four times radical seven.
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If you don't mind, I'm just going to move this all up here.
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So square root of three times square root of four, which is two times radical seven.
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Three times two is six, radical seven.
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And that will be your final answer as several five, the square root of 18 times the square root of 14.