[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:01.29,0:00:04.27,Default,,0000,0000,0000,,Welcome to the presentation\Non simplifying radicals.
Dialogue: 0,0:00:04.27,0:00:06.48,Default,,0000,0000,0000,,So let's get started with getting a little terminology out of the way.
Dialogue: 0,0:00:06.49,0:00:11.34,Default,,0000,0000,0000,,You're probably just wondering what a radical is and I'll just let you know.
Dialogue: 0,0:00:11.34,0:00:13.11,Default,,0000,0000,0000,,I've got to get the pen settings right.
Dialogue: 0,0:00:13.11,0:00:15.28,Default,,0000,0000,0000,,A radical is just that.
Dialogue: 0,0:00:15.28,0:00:18.81,Default,,0000,0000,0000,,Or you're probably more familiar calling that the square root symbol.
Dialogue: 0,0:00:18.81,0:00:20.57,Default,,0000,0000,0000,,So with the terminology out of\Nthe way,
Dialogue: 0,0:00:20.57,0:00:23.88,Default,,0000,0000,0000,,let's actually talk about what it means to simplify a radical.
Dialogue: 0,0:00:23.88,0:00:25.73,Default,,0000,0000,0000,,And some people would argue that what we're going to actually be doing
Dialogue: 0,0:00:25.73,0:00:26.89,Default,,0000,0000,0000,,is actually making it more complicated.
Dialogue: 0,0:00:26.89,0:00:29.46,Default,,0000,0000,0000,,But let's see.
Dialogue: 0,0:00:29.46,0:00:32.82,Default,,0000,0000,0000,,Let me erase that.
Dialogue: 0,0:00:32.82,0:00:36.90,Default,,0000,0000,0000,,So if I were to give you the square root of 36,
Dialogue: 0,0:00:36.90,0:00:37.61,Default,,0000,0000,0000,,you'd say hey, that's easy.
Dialogue: 0,0:00:37.61,0:00:40.18,Default,,0000,0000,0000,,That's just equal to 6 times 6
Dialogue: 0,0:00:40.18,0:00:43.85,Default,,0000,0000,0000,,or you'd say the square root of 36 is just 6.
Dialogue: 0,0:00:43.85,0:00:50.68,Default,,0000,0000,0000,,Now, what if I asked you what\Nthe square root of 72 is?
Dialogue: 0,0:00:50.68,0:00:54.59,Default,,0000,0000,0000,,Well, we know that\N72 is 36 times 2, right?
Dialogue: 0,0:00:54.59,0:00:55.68,Default,,0000,0000,0000,,So let's write that.
Dialogue: 0,0:00:55.68,0:01:04.36,Default,,0000,0000,0000,,Square root of 72 is the same thing as the square root of 36 times 2.
Dialogue: 0,0:01:04.37,0:01:07.99,Default,,0000,0000,0000,,Right? We just rewrote seventy-two as thirty-six times two.
Dialogue: 0,0:01:07.99,0:01:11.58,Default,,0000,0000,0000,,And the square root, if you remember from level 3 exponents.
Dialogue: 0,0:01:11.58,0:01:14.92,Default,,0000,0000,0000,,square root is the same thing as something to the one half power.
Dialogue: 0,0:01:14.92,0:01:15.86,Default,,0000,0000,0000,,So let's write it that way.
Dialogue: 0,0:01:15.86,0:01:20.28,Default,,0000,0000,0000,,And I'm just writing it this way just to show you how this radical simplification works,
Dialogue: 0,0:01:20.28,0:01:22.96,Default,,0000,0000,0000,,and that it's really not a new concept.
Dialogue: 0,0:01:22.98,0:01:29.49,Default,,0000,0000,0000,,So this is the same thing as\N36 times 2 to the one half power.
Dialogue: 0,0:01:29.49,0:01:33.21,Default,,0000,0000,0000,,Right? Because it's just a square root\Nis the same thing as one half power.
Dialogue: 0,0:01:33.21,0:01:37.29,Default,,0000,0000,0000,,And we learned from the exponent rules that when you multiply two numbers
Dialogue: 0,0:01:37.29,0:01:39.88,Default,,0000,0000,0000,,and then you raise that to the one half power,
Dialogue: 0,0:01:39.88,0:01:47.10,Default,,0000,0000,0000,,that that's the same thing as raising each of the numbers to the one half power
Dialogue: 0,0:01:47.10,0:01:50.45,Default,,0000,0000,0000,,and then multiplying. Right?
Dialogue: 0,0:01:50.45,0:01:58.48,Default,,0000,0000,0000,,Well that right there, that's the same thing as saying the square root is 36 times the square root of 2.
Dialogue: 0,0:01:58.48,0:02:00.78,Default,,0000,0000,0000,,And we already figured out what\Nthe square root of 36 is.
Dialogue: 0,0:02:00.78,0:02:01.81,Default,,0000,0000,0000,,It's 6.
Dialogue: 0,0:02:01.81,0:02:07.95,Default,,0000,0000,0000,,So that just equals 6 times\Nthe square root of 2.
Dialogue: 0,0:02:07.95,0:02:11.57,Default,,0000,0000,0000,,And you're probably wondering why I went through this step of changing the radical,
Dialogue: 0,0:02:11.57,0:02:13.52,Default,,0000,0000,0000,,the square root symbol, into the one half power.
Dialogue: 0,0:02:13.53,0:02:17.02,Default,,0000,0000,0000,,And I did that just to show you that this is just an extension of the exponent rules.
Dialogue: 0,0:02:17.02,0:02:19.04,Default,,0000,0000,0000,,It isn't really a new concept.
Dialogue: 0,0:02:19.04,0:02:24.69,Default,,0000,0000,0000,,Although, I guess sometimes it's not so obvious that\Nthey are the same concepts.
Dialogue: 0,0:02:24.69,0:02:26.48,Default,,0000,0000,0000,,I just wanted to\Npoint that out.
Dialogue: 0,0:02:26.48,0:02:28.47,Default,,0000,0000,0000,,So let's do another problem.
Dialogue: 0,0:02:28.47,0:02:33.25,Default,,0000,0000,0000,,I think as we do more and more problems, these will become more obvious.
Dialogue: 0,0:02:33.25,0:02:37.82,Default,,0000,0000,0000,,The square root of 50.
Dialogue: 0,0:02:37.82,0:02:40.03,Default,,0000,0000,0000,,Well, the square root of 50 --
Dialogue: 0,0:02:40.03,0:02:47.15,Default,,0000,0000,0000,,50 is the same thing as 25 times 2.
Dialogue: 0,0:02:47.15,0:02:51.65,Default,,0000,0000,0000,,And we know, based on what we just did and this is really just an exponent rule,
Dialogue: 0,0:02:51.65,0:02:58.41,Default,,0000,0000,0000,,The square root of 25 times 2 is the same thing as the square root of 25
Dialogue: 0,0:02:58.41,0:03:01.07,Default,,0000,0000,0000,,times the square root of 2.
Dialogue: 0,0:03:01.07,0:03:02.58,Default,,0000,0000,0000,,Well we know what the\Nsquare root of 25 is.
Dialogue: 0,0:03:02.58,0:03:03.17,Default,,0000,0000,0000,,That's 5.
Dialogue: 0,0:03:03.17,0:03:09.70,Default,,0000,0000,0000,,So that just equals 5 times\Nthe square root of 2.
Dialogue: 0,0:03:09.70,0:03:14.15,Default,,0000,0000,0000,,Now, you might be saying, "Hey,\NSal, you make it look easy,
Dialogue: 0,0:03:14.15,0:03:17.86,Default,,0000,0000,0000,,but how did you know to split 50\Ninto 25 and 2?"
Dialogue: 0,0:03:17.86,0:03:23.10,Default,,0000,0000,0000,,Why didn't I say that 50 is equal to the square root of 5 and 10?
Dialogue: 0,0:03:23.10,0:03:28.80,Default,,0000,0000,0000,,Or that 50 is equal to the square root\N-- actually, I think 1 and 50?
Dialogue: 0,0:03:28.80,0:03:30.53,Default,,0000,0000,0000,,I don't know what\Nother factors 50 has.
Dialogue: 0,0:03:30.53,0:03:32.57,Default,,0000,0000,0000,,Well, anyway, I won't go\Ninto that right now.
Dialogue: 0,0:03:32.57,0:03:37.05,Default,,0000,0000,0000,,The reason why I picked 25 and\N2 is because I wanted a factor of 50--
Dialogue: 0,0:03:37.05,0:03:40.87,Default,,0000,0000,0000,,I actually wanted the largest factor of 50 that is a perfect square.
Dialogue: 0,0:03:40.88,0:03:42.86,Default,,0000,0000,0000,,And that's 25.
Dialogue: 0,0:03:42.86,0:03:45.86,Default,,0000,0000,0000,,If I had done 5 and 10, there's really nothing I could have done with it,
Dialogue: 0,0:03:45.86,0:03:47.99,Default,,0000,0000,0000,,because neither 5 nor 10 are perfect squares
Dialogue: 0,0:03:47.99,0:03:50.61,Default,,0000,0000,0000,,and the same thing's with 1 and 50.
Dialogue: 0,0:03:50.61,0:03:51.84,Default,,0000,0000,0000,,So the way you should think\Nabout it,
Dialogue: 0,0:03:51.84,0:03:55.05,Default,,0000,0000,0000,,think about the factors of the original number
Dialogue: 0,0:03:55.05,0:03:57.89,Default,,0000,0000,0000,,and figure out if any of those factors are perfect squares.
Dialogue: 0,0:03:57.89,0:03:59.37,Default,,0000,0000,0000,,And there's no real\Nmechanical way.
Dialogue: 0,0:03:59.37,0:04:02.28,Default,,0000,0000,0000,,You really just have to learn\Nto recognize perfect squares.
Dialogue: 0,0:04:02.28,0:04:03.94,Default,,0000,0000,0000,,And you'll get familiar\Nwith them, of course.
Dialogue: 0,0:04:03.94,0:04:17.87,Default,,0000,0000,0000,,They're 1, 4, 9, 25, 16,\N25, 36, 49, 64, et cetera.
Dialogue: 0,0:04:17.87,0:04:21.29,Default,,0000,0000,0000,,And maybe by doing this module, you'll actually learn to recognize them more readily.
Dialogue: 0,0:04:21.29,0:04:26.64,Default,,0000,0000,0000,,But if any of these numbers are a factor of the number under the radical sign
Dialogue: 0,0:04:26.64,0:04:28.04,Default,,0000,0000,0000,,then you'll probably want to factor them out.
Dialogue: 0,0:04:28.04,0:04:30.08,Default,,0000,0000,0000,,And then you can take them out of the radical sign
Dialogue: 0,0:04:30.08,0:04:32.62,Default,,0000,0000,0000,,like we did up in this problem.
Dialogue: 0,0:04:32.62,0:04:37.59,Default,,0000,0000,0000,,Let's do a couple more.
Dialogue: 0,0:04:37.59,0:04:43.46,Default,,0000,0000,0000,,What is 7 times the square root of 27?
Dialogue: 0,0:04:43.47,0:04:45.07,Default,,0000,0000,0000,,And when I write the 7 right\Nnext to it,
Dialogue: 0,0:04:45.07,0:04:47.72,Default,,0000,0000,0000,,that just means times the square root of 27.
Dialogue: 0,0:04:47.72,0:04:50.50,Default,,0000,0000,0000,,Well, let's think about what\Nother factors of 27 are,
Dialogue: 0,0:04:50.50,0:04:52.05,Default,,0000,0000,0000,,and whether any of them are a perfect square.
Dialogue: 0,0:04:52.05,0:04:56.71,Default,,0000,0000,0000,,Well, 3 is a factor of 27, but\Nthat's not a perfect square.
Dialogue: 0,0:04:56.71,0:04:58.26,Default,,0000,0000,0000,,9 is.
Dialogue: 0,0:04:58.26,0:05:01.22,Default,,0000,0000,0000,,So, we could say 7 --
Dialogue: 0,0:05:01.22,0:05:08.78,Default,,0000,0000,0000,,that's equal to 7 times the square root of 9 times 3.
Dialogue: 0,0:05:08.78,0:05:11.35,Default,,0000,0000,0000,,And now, based on the rules we just learned,
Dialogue: 0,0:05:11.35,0:05:17.57,Default,,0000,0000,0000,,that's the same thing as 7 times the square\Nroot of 9
Dialogue: 0,0:05:17.57,0:05:21.14,Default,,0000,0000,0000,,times the square root of 3.
Dialogue: 0,0:05:21.14,0:05:26.40,Default,,0000,0000,0000,,Well that just equals 7 times 3\Nbecause the square root of 9 is 3
Dialogue: 0,0:05:26.40,0:05:29.27,Default,,0000,0000,0000,,times the square root of 3.
Dialogue: 0,0:05:29.27,0:05:34.67,Default,,0000,0000,0000,,That equals 21 times\Nthe square root of 3.
Dialogue: 0,0:05:34.67,0:05:35.83,Default,,0000,0000,0000,,Done.
Dialogue: 0,0:05:35.83,0:05:37.92,Default,,0000,0000,0000,,Let's do another one.
Dialogue: 0,0:05:37.92,0:05:46.08,Default,,0000,0000,0000,,What is nine times the square root of eighteen?
Dialogue: 0,0:05:46.08,0:05:48.41,Default,,0000,0000,0000,,Well, once again, what are the factors of eighteen?
Dialogue: 0,0:05:48.41,0:05:50.52,Default,,0000,0000,0000,,Well do we have 6 and 3?
Dialogue: 0,0:05:50.52,0:05:52.28,Default,,0000,0000,0000,,1 and 18?
Dialogue: 0,0:05:52.28,0:05:54.55,Default,,0000,0000,0000,,None of the numbers I mentioned\Nso far are perfect squares.
Dialogue: 0,0:05:54.55,0:05:56.54,Default,,0000,0000,0000,,But we also have 2 and 9.
Dialogue: 0,0:05:56.54,0:05:59.01,Default,,0000,0000,0000,,And 9 is a perfect square.
Dialogue: 0,0:05:59.01,0:05:59.77,Default,,0000,0000,0000,,So let's write that.
Dialogue: 0,0:05:59.77,0:06:07.02,Default,,0000,0000,0000,,That's equal to 9 times the\Nsquare root of 2 times 9.
Dialogue: 0,0:06:07.02,0:06:11.56,Default,,0000,0000,0000,,Which is equal to 9 times the\Nsquare root of 2 --
Dialogue: 0,0:06:11.56,0:06:15.58,Default,,0000,0000,0000,,that's a 2, times the square root of 9.
Dialogue: 0,0:06:15.58,0:06:20.30,Default,,0000,0000,0000,,Which equals 9 times the square\Nroot of 2 times 3, right?
Dialogue: 0,0:06:20.31,0:06:22.83,Default,,0000,0000,0000,,That's the square root of 9 which equals
Dialogue: 0,0:06:22.83,0:06:27.25,Default,,0000,0000,0000,,27 times the square root of 2.
Dialogue: 0,0:06:27.25,0:06:28.13,Default,,0000,0000,0000,,There we go.
Dialogue: 0,0:06:28.13,0:06:30.16,Default,,0000,0000,0000,,Hopefully, you're starting to\Nget the hang of these problems.
Dialogue: 0,0:06:30.16,0:06:33.07,Default,,0000,0000,0000,,Let's do another one.
Dialogue: 0,0:06:33.07,0:06:40.02,Default,,0000,0000,0000,,What is 4 times the\Nsquare root of 25?
Dialogue: 0,0:06:40.02,0:06:41.88,Default,,0000,0000,0000,,Well, twenty-five itself is a perfect square.
Dialogue: 0,0:06:41.88,0:06:45.09,Default,,0000,0000,0000,,This is kind of a problem that's so easy that it's a bit of a trick problem.
Dialogue: 0,0:06:45.11,0:06:47.25,Default,,0000,0000,0000,,25 itself is a perfect square.
Dialogue: 0,0:06:47.25,0:06:51.20,Default,,0000,0000,0000,,The square root is 5, so this is just equal to 4 times 5,
Dialogue: 0,0:06:51.20,0:06:52.91,Default,,0000,0000,0000,,which is equal to 20.
Dialogue: 0,0:06:52.91,0:06:57.02,Default,,0000,0000,0000,,Square root of 25 is 5.
Dialogue: 0,0:06:57.02,0:06:58.22,Default,,0000,0000,0000,,Let's do another one.
Dialogue: 0,0:06:58.22,0:07:04.69,Default,,0000,0000,0000,,What's 3 times the\Nsquare root of 29?
Dialogue: 0,0:07:04.69,0:07:06.19,Default,,0000,0000,0000,,Well 29 only has two factors.
Dialogue: 0,0:07:06.19,0:07:06.87,Default,,0000,0000,0000,,It's a prime number.
Dialogue: 0,0:07:06.87,0:07:09.45,Default,,0000,0000,0000,,It only has the\Nfactors 1 and 29.
Dialogue: 0,0:07:09.45,0:07:11.75,Default,,0000,0000,0000,,And neither of those numbers\Nare perfect squares.
Dialogue: 0,0:07:11.75,0:07:14.22,Default,,0000,0000,0000,,So we really can't simplify\Nthis one anymore.
Dialogue: 0,0:07:14.22,0:07:19.34,Default,,0000,0000,0000,,So, this is already in\Ncompletely simplified form.
Dialogue: 0,0:07:19.34,0:07:21.36,Default,,0000,0000,0000,,Let's do a couple more.
Dialogue: 0,0:07:21.36,0:07:32.13,Default,,0000,0000,0000,,What about 7 times the square root of 320?
Dialogue: 0,0:07:32.14,0:07:35.70,Default,,0000,0000,0000,,So, let's think about 320.
Dialogue: 0,0:07:35.70,0:07:39.80,Default,,0000,0000,0000,,Well we could actually do it in steps when we have larger numbers like this.
Dialogue: 0,0:07:39.81,0:07:43.29,Default,,0000,0000,0000,,I can look at it and say, well\Nit does look like 4 --
Dialogue: 0,0:07:43.29,0:07:47.38,Default,,0000,0000,0000,,actually it looks like 16 would go into this because 16 goes into 32.
Dialogue: 0,0:07:47.38,0:07:48.38,Default,,0000,0000,0000,,So let's try that.
Dialogue: 0,0:07:48.38,0:07:58.00,Default,,0000,0000,0000,,So that equals 7 times the\Nsquare root of 16 times 20.
Dialogue: 0,0:07:58.00,0:08:04.29,Default,,0000,0000,0000,,Well, that just equals 7 times the square root of 16
Dialogue: 0,0:08:04.29,0:08:06.96,Default,,0000,0000,0000,,times the square root of 20.
Dialogue: 0,0:08:06.96,0:08:08.59,Default,,0000,0000,0000,,7 times the square root of 16.
Dialogue: 0,0:08:08.59,0:08:10.38,Default,,0000,0000,0000,,The square root of 16 is 4.
Dialogue: 0,0:08:10.38,0:08:11.63,Default,,0000,0000,0000,,So 7 times 4 is 28.
Dialogue: 0,0:08:11.63,0:08:17.11,Default,,0000,0000,0000,,So that's 28 times the\Nsquare root of 20.
Dialogue: 0,0:08:17.11,0:08:19.10,Default,,0000,0000,0000,,Now are we done?
Dialogue: 0,0:08:19.10,0:08:21.80,Default,,0000,0000,0000,,Well actually, I think I can factor 20 even more
Dialogue: 0,0:08:21.80,0:08:24.68,Default,,0000,0000,0000,,because 20 is equal to 4 times 5.
Dialogue: 0,0:08:24.68,0:08:33.56,Default,,0000,0000,0000,,So I can say this is equal to 28 times the square root of 4 times 5.
Dialogue: 0,0:08:33.57,0:08:38.27,Default,,0000,0000,0000,,The square root of 4 is 2 so\Nthat could just take the 2 out
Dialogue: 0,0:08:38.27,0:08:43.66,Default,,0000,0000,0000,,and that becomes 56 times\Nthe square root of 5.
Dialogue: 0,0:08:43.66,0:08:44.45,Default,,0000,0000,0000,,I hope that made sense to you.
Dialogue: 0,0:08:44.45,0:08:45.98,Default,,0000,0000,0000,,And this is actually a\Npretty important technique
Dialogue: 0,0:08:45.98,0:08:46.89,Default,,0000,0000,0000,,I just did here.
Dialogue: 0,0:08:46.89,0:08:49.06,Default,,0000,0000,0000,,Immediately when I look at 320.
Dialogue: 0,0:08:49.06,0:08:52.16,Default,,0000,0000,0000,,I don't know what the largest\Nnumber is that goes into 320.
Dialogue: 0,0:08:52.16,0:08:54.15,Default,,0000,0000,0000,,It actually turns\Nout that it's 64.
Dialogue: 0,0:08:54.15,0:08:57.60,Default,,0000,0000,0000,,But just looking at the number, I said, well I know that 4 goes into it.
Dialogue: 0,0:08:57.61,0:08:59.70,Default,,0000,0000,0000,,So I could have just pulled out 4,
Dialogue: 0,0:08:59.70,0:09:01.63,Default,,0000,0000,0000,,and then said, "Oh, that's equal to 4 times 80."
Dialogue: 0,0:09:01.63,0:09:03.21,Default,,0000,0000,0000,,And then I would have had to work with 80.
Dialogue: 0,0:09:03.21,0:09:06.48,Default,,0000,0000,0000,,In this case, I saw 32 and I was like, it looks like 16 goes into it
Dialogue: 0,0:09:06.48,0:09:08.66,Default,,0000,0000,0000,,and I factored out 16 first.
Dialogue: 0,0:09:08.66,0:09:11.89,Default,,0000,0000,0000,,And when I took out the square root of 16, I multiplied the outside by 4
Dialogue: 0,0:09:11.89,0:09:13.16,Default,,0000,0000,0000,,and that's how I got the 28.
Dialogue: 0,0:09:13.16,0:09:15.28,Default,,0000,0000,0000,,But then I reduced the number\Non the inside and said,
Dialogue: 0,0:09:15.28,0:09:17.43,Default,,0000,0000,0000,,"Oh, well that still is divisible by a perfect square.
Dialogue: 0,0:09:17.43,0:09:20.06,Default,,0000,0000,0000,,It's still divisible by 4." And\Nthen I kept doing it
Dialogue: 0,0:09:20.06,0:09:27.70,Default,,0000,0000,0000,,until I was left with essentially, a prime number or a number that couldn't be reduced anymore under the radical.
Dialogue: 0,0:09:27.70,0:09:29.95,Default,,0000,0000,0000,,And it actually doesn't\Nhave to be prime.
Dialogue: 0,0:09:29.95,0:09:34.23,Default,,0000,0000,0000,,So hopefully, that gives you a good sense of how to do radical simplification.
Dialogue: 0,0:09:34.23,0:09:37.85,Default,,0000,0000,0000,,It's really just an extension of the exponent rules that you've already learned,
Dialogue: 0,0:09:37.85,0:09:41.87,Default,,0000,0000,0000,,and hopefully as you do the module, you'll get good at it.
Dialogue: 0,0:09:41.89,0:09:43.42,Default,,0000,0000,0000,,Have fun!