[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.53,0:00:03.22,Default,,0000,0000,0000,,In this video we're going\Nto get introduced to the
Dialogue: 0,0:00:03.22,0:00:14.19,Default,,0000,0000,0000,,Pythagorean theorem,\Nwhich is fun on its own.
Dialogue: 0,0:00:14.19,0:00:16.93,Default,,0000,0000,0000,,But you'll see as you learn\Nmore and more mathematics it's
Dialogue: 0,0:00:16.93,0:00:21.57,Default,,0000,0000,0000,,one of those cornerstone\Ntheorems of really all of math.
Dialogue: 0,0:00:21.57,0:00:24.92,Default,,0000,0000,0000,,It's useful in geometry,\Nit's kind of the backbone
Dialogue: 0,0:00:24.92,0:00:26.75,Default,,0000,0000,0000,,of trigonometry.
Dialogue: 0,0:00:26.75,0:00:29.20,Default,,0000,0000,0000,,You're also going to use\Nit to calculate distances
Dialogue: 0,0:00:29.20,0:00:30.51,Default,,0000,0000,0000,,between points.
Dialogue: 0,0:00:30.51,0:00:33.81,Default,,0000,0000,0000,,So it's a good thing to really\Nmake sure we know well.
Dialogue: 0,0:00:33.81,0:00:35.57,Default,,0000,0000,0000,,So enough talk on my end.
Dialogue: 0,0:00:35.57,0:00:38.32,Default,,0000,0000,0000,,Let me tell you what the\NPythagorean theorem is.
Dialogue: 0,0:00:38.32,0:00:43.29,Default,,0000,0000,0000,,So if we have a triangle, and\Nthe triangle has to be a right
Dialogue: 0,0:00:43.29,0:00:49.11,Default,,0000,0000,0000,,triangle, which means that one\Nof the three angles in the
Dialogue: 0,0:00:49.11,0:00:51.52,Default,,0000,0000,0000,,triangle have to be 90 degrees.
Dialogue: 0,0:00:51.52,0:00:54.58,Default,,0000,0000,0000,,And you specify that it's\N90 degrees by drawing that
Dialogue: 0,0:00:54.58,0:00:55.93,Default,,0000,0000,0000,,little box right there.
Dialogue: 0,0:00:55.93,0:00:58.83,Default,,0000,0000,0000,,So that right there is-- let\Nme do this in a different
Dialogue: 0,0:00:58.83,0:01:05.55,Default,,0000,0000,0000,,color-- a 90 degree angle.
Dialogue: 0,0:01:05.55,0:01:09.93,Default,,0000,0000,0000,,Or, we could call\Nit a right angle.
Dialogue: 0,0:01:09.93,0:01:13.39,Default,,0000,0000,0000,,And a triangle that has\Na right angle in it is
Dialogue: 0,0:01:13.39,0:01:15.85,Default,,0000,0000,0000,,called a right triangle.
Dialogue: 0,0:01:15.85,0:01:21.70,Default,,0000,0000,0000,,So this is called\Na right triangle.
Dialogue: 0,0:01:21.70,0:01:25.44,Default,,0000,0000,0000,,Now, with the Pythagorean\Ntheorem, if we know two sides
Dialogue: 0,0:01:25.44,0:01:28.98,Default,,0000,0000,0000,,of a right triangle we can\Nalways figure out
Dialogue: 0,0:01:28.98,0:01:30.92,Default,,0000,0000,0000,,the third side.
Dialogue: 0,0:01:30.92,0:01:34.31,Default,,0000,0000,0000,,And before I show you how to\Ndo that, let me give you one
Dialogue: 0,0:01:34.31,0:01:36.56,Default,,0000,0000,0000,,more piece of terminology.
Dialogue: 0,0:01:36.56,0:01:43.23,Default,,0000,0000,0000,,The longest side of a right\Ntriangle is the side opposite
Dialogue: 0,0:01:43.23,0:01:46.69,Default,,0000,0000,0000,,the 90 degree angle-- or\Nopposite the right angle.
Dialogue: 0,0:01:46.69,0:01:49.65,Default,,0000,0000,0000,,So in this case it is\Nthis side right here.
Dialogue: 0,0:01:49.65,0:01:51.28,Default,,0000,0000,0000,,This is the longest side.
Dialogue: 0,0:01:51.28,0:01:55.02,Default,,0000,0000,0000,,And the way to figure out where\Nthat right triangle is, and
Dialogue: 0,0:01:55.02,0:01:58.06,Default,,0000,0000,0000,,kind of it opens into\Nthat longest side.
Dialogue: 0,0:01:58.06,0:02:00.15,Default,,0000,0000,0000,,That longest side is\Ncalled the hypotenuse.
Dialogue: 0,0:02:03.13,0:02:05.33,Default,,0000,0000,0000,,And it's good to know, because\Nwe'll keep referring to it.
Dialogue: 0,0:02:05.33,0:02:09.00,Default,,0000,0000,0000,,And just so we always are good\Nat identifying the hypotenuse,
Dialogue: 0,0:02:09.00,0:02:12.56,Default,,0000,0000,0000,,let me draw a couple of\Nmore right triangles.
Dialogue: 0,0:02:12.56,0:02:17.09,Default,,0000,0000,0000,,So let's say I have a triangle\Nthat looks like that.
Dialogue: 0,0:02:17.09,0:02:19.39,Default,,0000,0000,0000,,Let me draw it a\Nlittle bit nicer.
Dialogue: 0,0:02:19.39,0:02:22.13,Default,,0000,0000,0000,,So let's say I have a triangle\Nthat looks like that.
Dialogue: 0,0:02:22.13,0:02:24.01,Default,,0000,0000,0000,,And I were to tell you\Nthat this angle right
Dialogue: 0,0:02:24.01,0:02:25.39,Default,,0000,0000,0000,,here is 90 degrees.
Dialogue: 0,0:02:25.39,0:02:29.86,Default,,0000,0000,0000,,In this situation this is the\Nhypotenuse, because it is
Dialogue: 0,0:02:29.86,0:02:33.41,Default,,0000,0000,0000,,opposite the 90 degree angle.
Dialogue: 0,0:02:33.41,0:02:34.88,Default,,0000,0000,0000,,It is the longest side.
Dialogue: 0,0:02:34.88,0:02:36.67,Default,,0000,0000,0000,,Let me do one more, just\Nso that we're good at
Dialogue: 0,0:02:36.67,0:02:39.42,Default,,0000,0000,0000,,recognizing the hypotenuse.
Dialogue: 0,0:02:39.42,0:02:44.05,Default,,0000,0000,0000,,So let's say that that is my\Ntriangle, and this is the 90
Dialogue: 0,0:02:44.05,0:02:45.79,Default,,0000,0000,0000,,degree angle right there.
Dialogue: 0,0:02:45.79,0:02:47.71,Default,,0000,0000,0000,,And I think you know how\Nto do this already.
Dialogue: 0,0:02:47.71,0:02:49.62,Default,,0000,0000,0000,,You go right what\Nit opens into.
Dialogue: 0,0:02:49.62,0:02:51.53,Default,,0000,0000,0000,,That is the hypotenuse.
Dialogue: 0,0:02:51.53,0:02:53.20,Default,,0000,0000,0000,,That is the longest side.
Dialogue: 0,0:02:57.94,0:03:00.40,Default,,0000,0000,0000,,So once you have identified the\Nhypotenuse-- and let's say
Dialogue: 0,0:03:00.40,0:03:02.05,Default,,0000,0000,0000,,that that has length C.
Dialogue: 0,0:03:02.05,0:03:03.98,Default,,0000,0000,0000,,And now we're going to\Nlearn what the Pythagorean
Dialogue: 0,0:03:03.98,0:03:05.21,Default,,0000,0000,0000,,theorem tells us.
Dialogue: 0,0:03:05.21,0:03:08.68,Default,,0000,0000,0000,,So let's say that C is equal to\Nthe length of the hypotenuse.
Dialogue: 0,0:03:08.68,0:03:11.63,Default,,0000,0000,0000,,So let's call this\NC-- that side is C.
Dialogue: 0,0:03:11.63,0:03:17.91,Default,,0000,0000,0000,,Let's call this side\Nright over here A.
Dialogue: 0,0:03:17.91,0:03:21.89,Default,,0000,0000,0000,,And let's call this\Nside over here B.
Dialogue: 0,0:03:21.89,0:03:28.62,Default,,0000,0000,0000,,So the Pythagorean theorem\Ntells us that A squared-- so
Dialogue: 0,0:03:28.62,0:03:32.88,Default,,0000,0000,0000,,the length of one of the\Nshorter sides squared-- plus
Dialogue: 0,0:03:32.88,0:03:36.89,Default,,0000,0000,0000,,the length of the other shorter\Nside squared is going to
Dialogue: 0,0:03:36.89,0:03:41.37,Default,,0000,0000,0000,,be equal to the length of\Nthe hypotenuse squared.
Dialogue: 0,0:03:41.37,0:03:43.74,Default,,0000,0000,0000,,Now let's do that with an\Nactual problem, and you'll see
Dialogue: 0,0:03:43.74,0:03:45.82,Default,,0000,0000,0000,,that it's actually not so bad.
Dialogue: 0,0:03:45.82,0:03:49.82,Default,,0000,0000,0000,,So let's say that I have a\Ntriangle that looks like this.
Dialogue: 0,0:03:49.82,0:03:51.05,Default,,0000,0000,0000,,Let me draw it.
Dialogue: 0,0:03:51.05,0:03:54.21,Default,,0000,0000,0000,,Let's say this is my triangle.
Dialogue: 0,0:03:54.21,0:03:57.16,Default,,0000,0000,0000,,It looks something like this.
Dialogue: 0,0:03:57.16,0:04:00.56,Default,,0000,0000,0000,,And let's say that they tell us\Nthat this is the right angle.
Dialogue: 0,0:04:00.56,0:04:02.94,Default,,0000,0000,0000,,That this length right here--\Nlet me do this in different
Dialogue: 0,0:04:02.94,0:04:06.83,Default,,0000,0000,0000,,colors-- this length right\Nhere is 3, and that this
Dialogue: 0,0:04:06.83,0:04:09.17,Default,,0000,0000,0000,,length right here is 4.
Dialogue: 0,0:04:09.17,0:04:14.49,Default,,0000,0000,0000,,And they want us to figure\Nout that length right there.
Dialogue: 0,0:04:14.49,0:04:17.13,Default,,0000,0000,0000,,Now the first thing you want to\Ndo, before you even apply the
Dialogue: 0,0:04:17.13,0:04:19.66,Default,,0000,0000,0000,,Pythagorean theorem, is to\Nmake sure you have your
Dialogue: 0,0:04:19.66,0:04:20.71,Default,,0000,0000,0000,,hypotenuse straight.
Dialogue: 0,0:04:20.71,0:04:23.35,Default,,0000,0000,0000,,You make sure you know\Nwhat you're solving for.
Dialogue: 0,0:04:23.35,0:04:26.12,Default,,0000,0000,0000,,And in this circumstance we're\Nsolving for the hypotenuse.
Dialogue: 0,0:04:26.12,0:04:30.44,Default,,0000,0000,0000,,And we know that because this\Nside over here, it is the side
Dialogue: 0,0:04:30.44,0:04:33.31,Default,,0000,0000,0000,,opposite the right angle.
Dialogue: 0,0:04:33.31,0:04:36.54,Default,,0000,0000,0000,,If we look at the Pythagorean\Ntheorem, this is C.
Dialogue: 0,0:04:36.54,0:04:38.16,Default,,0000,0000,0000,,This is the longest side.
Dialogue: 0,0:04:38.16,0:04:41.92,Default,,0000,0000,0000,,So now we're ready to apply\Nthe Pythagorean theorem.
Dialogue: 0,0:04:41.92,0:04:48.07,Default,,0000,0000,0000,,It tells us that 4 squared--\None of the shorter sides-- plus
Dialogue: 0,0:04:48.07,0:04:53.26,Default,,0000,0000,0000,,3 squared-- the square of\Nanother of the shorter sides--
Dialogue: 0,0:04:53.26,0:04:56.08,Default,,0000,0000,0000,,is going to be equal to this\Nlonger side squared-- the
Dialogue: 0,0:04:56.08,0:05:00.59,Default,,0000,0000,0000,,hypotenuse squared-- is going\Nto be equal to C squared.
Dialogue: 0,0:05:00.59,0:05:02.31,Default,,0000,0000,0000,,And then you just solve for C.
Dialogue: 0,0:05:02.31,0:05:06.38,Default,,0000,0000,0000,,So 4 squared is the same\Nthing as 4 times 4.
Dialogue: 0,0:05:06.38,0:05:08.46,Default,,0000,0000,0000,,That is 16.
Dialogue: 0,0:05:08.46,0:05:11.91,Default,,0000,0000,0000,,And 3 squared is the same\Nthing as 3 times 3.
Dialogue: 0,0:05:11.91,0:05:13.81,Default,,0000,0000,0000,,So that is 9.
Dialogue: 0,0:05:13.81,0:05:18.58,Default,,0000,0000,0000,,And that is going to be\Nequal to C squared.
Dialogue: 0,0:05:18.58,0:05:20.61,Default,,0000,0000,0000,,Now what is 16 plus 9?
Dialogue: 0,0:05:20.61,0:05:22.48,Default,,0000,0000,0000,,It's 25.
Dialogue: 0,0:05:22.48,0:05:25.20,Default,,0000,0000,0000,,So 25 is equal to C squared.
Dialogue: 0,0:05:25.20,0:05:29.02,Default,,0000,0000,0000,,And we could take the positive\Nsquare root of both sides.
Dialogue: 0,0:05:29.02,0:05:30.96,Default,,0000,0000,0000,,I guess, just if you look at\Nit mathematically, it could
Dialogue: 0,0:05:30.96,0:05:33.16,Default,,0000,0000,0000,,be negative 5 as well.
Dialogue: 0,0:05:33.16,0:05:34.87,Default,,0000,0000,0000,,But we're dealing with\Ndistances, so we only care
Dialogue: 0,0:05:34.87,0:05:37.05,Default,,0000,0000,0000,,about the positive roots.
Dialogue: 0,0:05:37.05,0:05:41.17,Default,,0000,0000,0000,,So you take the principal\Nroot of both sides and
Dialogue: 0,0:05:41.17,0:05:44.28,Default,,0000,0000,0000,,you get 5 is equal to C.
Dialogue: 0,0:05:44.28,0:05:50.26,Default,,0000,0000,0000,,Or, the length of the\Nlongest side is equal to 5.
Dialogue: 0,0:05:50.26,0:05:52.64,Default,,0000,0000,0000,,Now, you can use the\NPythagorean theorem, if we give
Dialogue: 0,0:05:52.64,0:05:54.62,Default,,0000,0000,0000,,you two of the sides, to figure\Nout the third side no matter
Dialogue: 0,0:05:54.62,0:05:55.69,Default,,0000,0000,0000,,what the third side is.
Dialogue: 0,0:05:55.69,0:05:59.30,Default,,0000,0000,0000,,So let's do another\None right over here.
Dialogue: 0,0:05:59.30,0:06:10.67,Default,,0000,0000,0000,,Let's say that our\Ntriangle looks like this.
Dialogue: 0,0:06:10.67,0:06:12.61,Default,,0000,0000,0000,,And that is our right angle.
Dialogue: 0,0:06:12.61,0:06:17.82,Default,,0000,0000,0000,,Let's say this side over here\Nhas length 12, and let's say
Dialogue: 0,0:06:17.82,0:06:21.08,Default,,0000,0000,0000,,that this side over\Nhere has length 6.
Dialogue: 0,0:06:21.08,0:06:27.21,Default,,0000,0000,0000,,And we want to figure out this\Nlength right over there.
Dialogue: 0,0:06:27.21,0:06:29.87,Default,,0000,0000,0000,,Now, like I said, the first\Nthing you want to do is
Dialogue: 0,0:06:29.87,0:06:31.35,Default,,0000,0000,0000,,identify the hypotenuse.
Dialogue: 0,0:06:31.35,0:06:34.13,Default,,0000,0000,0000,,And that's going to be the side\Nopposite the right angle.
Dialogue: 0,0:06:34.13,0:06:35.55,Default,,0000,0000,0000,,We have the right angle here.
Dialogue: 0,0:06:35.55,0:06:37.65,Default,,0000,0000,0000,,You go opposite\Nthe right angle.
Dialogue: 0,0:06:37.65,0:06:41.46,Default,,0000,0000,0000,,The longest side, the\Nhypotenuse, is right there.
Dialogue: 0,0:06:41.46,0:06:46.10,Default,,0000,0000,0000,,So if we think about the\NPythagorean theorem-- that A
Dialogue: 0,0:06:46.10,0:06:50.82,Default,,0000,0000,0000,,squared plus B squared is\Nequal to C squared-- 12
Dialogue: 0,0:06:50.82,0:06:52.22,Default,,0000,0000,0000,,you could view as C.
Dialogue: 0,0:06:52.22,0:06:54.74,Default,,0000,0000,0000,,This is the hypotenuse.
Dialogue: 0,0:06:54.74,0:06:56.67,Default,,0000,0000,0000,,The C squared is the\Nhypotenuse squared.
Dialogue: 0,0:06:56.67,0:06:59.03,Default,,0000,0000,0000,,So you could say\N12 is equal to C.
Dialogue: 0,0:06:59.03,0:07:00.88,Default,,0000,0000,0000,,And then we could say that\Nthese sides, it doesn't matter
Dialogue: 0,0:07:00.88,0:07:02.58,Default,,0000,0000,0000,,whether you call one of\Nthem A or one of them B.
Dialogue: 0,0:07:02.58,0:07:04.97,Default,,0000,0000,0000,,So let's just call\Nthis side right here.
Dialogue: 0,0:07:04.97,0:07:06.99,Default,,0000,0000,0000,,Let's say A is equal to 6.
Dialogue: 0,0:07:06.99,0:07:11.78,Default,,0000,0000,0000,,And then we say B-- this\Ncolored B-- is equal
Dialogue: 0,0:07:11.78,0:07:12.64,Default,,0000,0000,0000,,to question mark.
Dialogue: 0,0:07:12.64,0:07:15.07,Default,,0000,0000,0000,,And now we can apply the\NPythagorean theorem.
Dialogue: 0,0:07:15.07,0:07:25.94,Default,,0000,0000,0000,,A squared, which is 6 squared,\Nplus the unknown B squared is
Dialogue: 0,0:07:25.94,0:07:28.33,Default,,0000,0000,0000,,equal to the hypotenuse\Nsquared-- is equal
Dialogue: 0,0:07:28.33,0:07:29.76,Default,,0000,0000,0000,,to C squared.
Dialogue: 0,0:07:29.76,0:07:33.25,Default,,0000,0000,0000,,Is equal to 12 squared.
Dialogue: 0,0:07:33.25,0:07:35.26,Default,,0000,0000,0000,,And now we can solve for B.
Dialogue: 0,0:07:35.26,0:07:36.37,Default,,0000,0000,0000,,And notice the difference here.
Dialogue: 0,0:07:36.37,0:07:38.11,Default,,0000,0000,0000,,Now we're not solving\Nfor the hypotenuse.
Dialogue: 0,0:07:38.11,0:07:40.21,Default,,0000,0000,0000,,We're solving for one\Nof the shorter sides.
Dialogue: 0,0:07:40.21,0:07:42.79,Default,,0000,0000,0000,,In the last example we\Nsolved for the hypotenuse.
Dialogue: 0,0:07:42.79,0:07:43.79,Default,,0000,0000,0000,,We solved for C.
Dialogue: 0,0:07:43.79,0:07:46.57,Default,,0000,0000,0000,,So that's why it's always\Nimportant to recognize that A
Dialogue: 0,0:07:46.57,0:07:49.19,Default,,0000,0000,0000,,squared plus B squared plus C\Nsquared, C is the length
Dialogue: 0,0:07:49.19,0:07:49.67,Default,,0000,0000,0000,,of the hypotenuse.
Dialogue: 0,0:07:49.67,0:07:51.85,Default,,0000,0000,0000,,So let's just solve for B here.
Dialogue: 0,0:07:51.85,0:07:59.28,Default,,0000,0000,0000,,So we get 6 squared is 36,\Nplus B squared, is equal
Dialogue: 0,0:07:59.28,0:08:04.70,Default,,0000,0000,0000,,to 12 squared-- this\N12 times 12-- is 144.
Dialogue: 0,0:08:04.70,0:08:08.55,Default,,0000,0000,0000,,Now we can subtract 36 from\Nboth sides of this equation.
Dialogue: 0,0:08:11.42,0:08:13.27,Default,,0000,0000,0000,,Those cancel out.
Dialogue: 0,0:08:13.27,0:08:17.51,Default,,0000,0000,0000,,On the left-hand side we're\Nleft with just a B squared
Dialogue: 0,0:08:17.51,0:08:23.41,Default,,0000,0000,0000,,is equal to-- now 144\Nminus 36 is what?
Dialogue: 0,0:08:23.41,0:08:27.00,Default,,0000,0000,0000,,144 minus 30 is 114.
Dialogue: 0,0:08:27.00,0:08:30.08,Default,,0000,0000,0000,,And then you\Nsubtract 6, is 108.
Dialogue: 0,0:08:30.08,0:08:33.91,Default,,0000,0000,0000,,So this is going to be 108.
Dialogue: 0,0:08:33.91,0:08:36.63,Default,,0000,0000,0000,,So that's what B squared is,\Nand now we want to take the
Dialogue: 0,0:08:36.63,0:08:40.60,Default,,0000,0000,0000,,principal root, or the\Npositive root, of both sides.
Dialogue: 0,0:08:40.60,0:08:44.43,Default,,0000,0000,0000,,And you get B is equal\Nto the square root, the
Dialogue: 0,0:08:44.43,0:08:48.65,Default,,0000,0000,0000,,principal root, of 108.
Dialogue: 0,0:08:48.65,0:08:50.55,Default,,0000,0000,0000,,Now let's see if we can\Nsimplify this a little bit.
Dialogue: 0,0:08:50.55,0:08:53.55,Default,,0000,0000,0000,,The square root of 108.
Dialogue: 0,0:08:53.55,0:08:54.93,Default,,0000,0000,0000,,And what we could do is\Nwe could take the prime
Dialogue: 0,0:08:54.93,0:08:56.67,Default,,0000,0000,0000,,factorization of 108\Nand see how we can
Dialogue: 0,0:08:56.67,0:08:58.41,Default,,0000,0000,0000,,simplify this radical.
Dialogue: 0,0:08:58.41,0:09:07.59,Default,,0000,0000,0000,,So 108 is the same thing as 2\Ntimes 54, which is the same
Dialogue: 0,0:09:07.59,0:09:15.57,Default,,0000,0000,0000,,thing as 2 times 27, which is\Nthe same thing as 3 times 9.
Dialogue: 0,0:09:15.57,0:09:19.78,Default,,0000,0000,0000,,So we have the square root of\N108 is the same thing as the
Dialogue: 0,0:09:19.78,0:09:24.55,Default,,0000,0000,0000,,square root of 2 times 2\Ntimes-- well actually,
Dialogue: 0,0:09:24.55,0:09:25.52,Default,,0000,0000,0000,,I'm not done.
Dialogue: 0,0:09:25.52,0:09:28.76,Default,,0000,0000,0000,,9 can be factorized\Ninto 3 times 3.
Dialogue: 0,0:09:28.76,0:09:34.17,Default,,0000,0000,0000,,So it's 2 times 2 times\N3 times 3 times 3.
Dialogue: 0,0:09:34.17,0:09:36.82,Default,,0000,0000,0000,,And so, we have a couple of\Nperfect squares in here.
Dialogue: 0,0:09:36.82,0:09:38.68,Default,,0000,0000,0000,,Let me rewrite it a\Nlittle bit neater.
Dialogue: 0,0:09:38.68,0:09:41.16,Default,,0000,0000,0000,,And this is all an exercise in\Nsimplifying radicals that you
Dialogue: 0,0:09:41.16,0:09:44.20,Default,,0000,0000,0000,,will bump into a lot while\Ndoing the Pythagorean theorem,
Dialogue: 0,0:09:44.20,0:09:46.46,Default,,0000,0000,0000,,so it doesn't hurt to\Ndo it right here.
Dialogue: 0,0:09:46.46,0:09:55.82,Default,,0000,0000,0000,,So this is the same thing as\Nthe square root of 2 times 2
Dialogue: 0,0:09:55.82,0:10:00.79,Default,,0000,0000,0000,,times 3 times 3 times the\Nsquare root of that last
Dialogue: 0,0:10:00.79,0:10:02.51,Default,,0000,0000,0000,,3 right over there.
Dialogue: 0,0:10:02.51,0:10:04.09,Default,,0000,0000,0000,,And this is the same thing.
Dialogue: 0,0:10:04.09,0:10:05.78,Default,,0000,0000,0000,,And, you know, you wouldn't\Nhave to do all of
Dialogue: 0,0:10:05.78,0:10:07.96,Default,,0000,0000,0000,,this on paper.
Dialogue: 0,0:10:07.96,0:10:08.97,Default,,0000,0000,0000,,You could do it in your head.
Dialogue: 0,0:10:08.97,0:10:09.53,Default,,0000,0000,0000,,What is this?
Dialogue: 0,0:10:09.53,0:10:11.78,Default,,0000,0000,0000,,2 times 2 is 4.
Dialogue: 0,0:10:11.78,0:10:14.20,Default,,0000,0000,0000,,4 times 9, this is 36.
Dialogue: 0,0:10:14.20,0:10:18.03,Default,,0000,0000,0000,,So this is the square root of\N36 times the square root of 3.
Dialogue: 0,0:10:18.03,0:10:20.61,Default,,0000,0000,0000,,The principal root of 36 is 6.
Dialogue: 0,0:10:20.61,0:10:25.38,Default,,0000,0000,0000,,So this simplifies to\N6 square roots of 3.
Dialogue: 0,0:10:25.38,0:10:28.73,Default,,0000,0000,0000,,So the length of B, you could\Nwrite it as the square root of
Dialogue: 0,0:10:28.73,0:10:34.04,Default,,0000,0000,0000,,108, or you could say it's\Nequal to 6 times the
Dialogue: 0,0:10:34.04,0:10:35.04,Default,,0000,0000,0000,,square root of 3.
Dialogue: 0,0:10:35.04,0:10:37.15,Default,,0000,0000,0000,,This is 12, this is 6.
Dialogue: 0,0:10:37.15,0:10:40.58,Default,,0000,0000,0000,,And the square root of 3,\Nwell this is going to be a 1
Dialogue: 0,0:10:40.58,0:10:41.60,Default,,0000,0000,0000,,point something something.
Dialogue: 0,0:10:41.60,0:10:45.36,Default,,0000,0000,0000,,So it's going to be a\Nlittle bit larger than 6.