WEBVTT
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Alright, for this problem what they're asking us to do is simplify this little expression
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here.
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So the first thing I do is I need to remember that we'll never have a negative number
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under a square root that we can rewrite it to be something like this.
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And the reason why I can rewrite it like that is just negative 9 times 9 is negative 9.
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But the reason why I did that is because I know that negative square root of negative
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1 equals our little friend I.
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So therefore I really don't need to write.
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I really need to write this.
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I can actually say that this is not going to be square root of 18 over and it's like
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I times square root 9.
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Now we know that the square root of 9 is going to be 3.
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So this is going to be square root of 18 over 3i.
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I haven't simplified my square root of 18 yet and that's just another point.
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I just want to make down.
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I'm going to add you a lot of things with this problem.
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Square root of 18 that can be reduced down to the square root of 9 times 2 as I factor
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it out.
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Well the square root of 9 is 3 times radical 2.
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Now we have an i on the bottom and we cannot divide by i on the bottom because we don't
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really know exactly what I represent.
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We know what I represent this radical square root of 9.
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Or remember you can't divide by a radical.
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So i is equal to square root of 9.
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You can't divide by a radical negative 1.
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So what I have to do is I'm going to have to get rid of that and actually let me rewrite
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this as 3 radical 2 over 3i.
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So what I'm going to have to do is to get rid of that i, I'm going to have to multiply
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by i on the top and the bottom.
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So what I'll be left with is 3 square root 2i over 3 times i squared.
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Now if I don't know what i squared is, I can do square root of 8 times 2.
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I obtain i squared.
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The square root of something squared can't allow.
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So therefore 3 times negative 1 is going to give me a negative 3.
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And I know that now these 2 can cancel out to leave me a negative square root of 2i.
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So I kind of went all the kind of old good place.
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You do have to make sure you simplify your square root of 18.
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You need to make sure you transfer your negative 9 or the square root of negative 9 to 3i.
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And then you also need to make sure you multiply your i over i to simplify your problem.