[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.65,0:00:03.75,Default,,0000,0000,0000,,We are asked to approximate the principle\Nroot,
Dialogue: 0,0:00:03.75,0:00:06.90,Default,,0000,0000,0000,,or the positive square root 45, to the\Nhundredths
Dialogue: 0,0:00:06.90,0:00:08.40,Default,,0000,0000,0000,,place, and I'm assuming they don't want us\Nto
Dialogue: 0,0:00:08.40,0:00:10.54,Default,,0000,0000,0000,,use a calculator because that would be too\Neasy.
Dialogue: 0,0:00:10.54,0:00:12.73,Default,,0000,0000,0000,,So let's see if we can approximate this,
Dialogue: 0,0:00:12.73,0:00:16.00,Default,,0000,0000,0000,,just with our pen and paper right over\Nhere.
Dialogue: 0,0:00:16.00,0:00:21.88,Default,,0000,0000,0000,,So square root of 45, so the square root\Nof 45, or the principle root of 45.
Dialogue: 0,0:00:21.88,0:00:27.34,Default,,0000,0000,0000,,45 is not a, 45 is not a perfect square.
Dialogue: 0,0:00:27.34,0:00:28.82,Default,,0000,0000,0000,,It's definitely not a perfect square.
Dialogue: 0,0:00:28.82,0:00:31.44,Default,,0000,0000,0000,,But, we know, let's see what are the\Nperfect squares around it?
Dialogue: 0,0:00:31.44,0:00:34.45,Default,,0000,0000,0000,,We know that it is going to be less than,
Dialogue: 0,0:00:34.45,0:00:37.98,Default,,0000,0000,0000,,the next perfect square above 45 is going\Nto be.
Dialogue: 0,0:00:37.98,0:00:41.49,Default,,0000,0000,0000,,Let's see it's going to be 49, because\Nthat is 7 times 7.
Dialogue: 0,0:00:41.49,0:00:44.12,Default,,0000,0000,0000,,So, it's less than the square to 49.
Dialogue: 0,0:00:44.12,0:00:46.75,Default,,0000,0000,0000,,and it's greater than, the square root of\N36.
Dialogue: 0,0:00:46.75,0:00:52.94,Default,,0000,0000,0000,,And so the square root of 36, the\Nprinciple root of 36 I should say, is
Dialogue: 0,0:00:52.94,0:00:59.48,Default,,0000,0000,0000,,6 and the principle root, the principle\Nroot of 49 is, 7.
Dialogue: 0,0:00:59.48,0:01:02.80,Default,,0000,0000,0000,,So this value right over here is going to\Nbe between.
Dialogue: 0,0:01:02.80,0:01:05.86,Default,,0000,0000,0000,,It's going to be between 6 and 7.
Dialogue: 0,0:01:05.86,0:01:08.81,Default,,0000,0000,0000,,And if we look at it, it's only 4 away
Dialogue: 0,0:01:08.81,0:01:13.70,Default,,0000,0000,0000,,from 49 and it's 9 away, it's 9 away from\N36.
Dialogue: 0,0:01:13.70,0:01:19.33,Default,,0000,0000,0000,,So it looks like, so the difference\Nbetween 36 and 49 is.
Dialogue: 0,0:01:19.33,0:01:24.19,Default,,0000,0000,0000,,It's 13, so it's a total 13 gap between\Nthe, 6 squared and
Dialogue: 0,0:01:24.19,0:01:28.41,Default,,0000,0000,0000,,7 squared and this is, this is 9 of the\Nway through it.
Dialogue: 0,0:01:28.41,0:01:31.37,Default,,0000,0000,0000,,So just as a kind of an approximation,\Nmaybe and it's not
Dialogue: 0,0:01:31.37,0:01:33.83,Default,,0000,0000,0000,,going to work out perfectly because we're\Nsquaring it, this isn't a
Dialogue: 0,0:01:33.83,0:01:37.85,Default,,0000,0000,0000,,linear relationship, but it's going to be\Ncloser to, 7 than it's
Dialogue: 0,0:01:37.85,0:01:41.33,Default,,0000,0000,0000,,going to be to 6 and it, at least the\Nsquare or the.
Dialogue: 0,0:01:41.33,0:01:44.29,Default,,0000,0000,0000,,45 is 9 13th of the way.
Dialogue: 0,0:01:44.29,0:01:48.78,Default,,0000,0000,0000,,So we could try, we could try, lets see,\Nit looks like a, that's about, that's
Dialogue: 0,0:01:48.78,0:01:55.89,Default,,0000,0000,0000,,about two thirds of the way, so lets try\N6.7, lets try 6.7 as a guess.
Dialogue: 0,0:01:55.89,0:01:59.99,Default,,0000,0000,0000,,Just based on, 0.7 it's about two thirds,\Nit looks like about the same.
Dialogue: 0,0:01:59.99,0:02:02.73,Default,,0000,0000,0000,,And actually we could calculate this right\Nhere if
Dialogue: 0,0:02:02.73,0:02:04.71,Default,,0000,0000,0000,,we want, actually let's do that just for\Nfun.
Dialogue: 0,0:02:04.71,0:02:07.57,Default,,0000,0000,0000,,So, 9 13th as a decimal is going to be\Nwhat.
Dialogue: 0,0:02:07.57,0:02:12.84,Default,,0000,0000,0000,,It's going to be 13 into 9 we are going to\Nput some decimal places
Dialogue: 0,0:02:12.84,0:02:18.27,Default,,0000,0000,0000,,right over here, 13 doesn't go into 9, 13\Ndoes go into 90 and it goes into
Dialogue: 0,0:02:18.27,0:02:24.16,Default,,0000,0000,0000,,90 as let's see it does go into 7 times It\Ngoes into it 6 times.
Dialogue: 0,0:02:24.16,0:02:28.93,Default,,0000,0000,0000,,So 6 times 3 is, 6 times 3 is 18.
Dialogue: 0,0:02:28.93,0:02:31.12,Default,,0000,0000,0000,,6 times one is 6 plus one is 7.
Dialogue: 0,0:02:31.12,0:02:34.63,Default,,0000,0000,0000,,And then you subtract and get twelve.
Dialogue: 0,0:02:34.63,0:02:39.51,Default,,0000,0000,0000,,So went into it almost exactly 7 times, so\Nthis value right here, almost 0.7.
Dialogue: 0,0:02:39.51,0:02:42.56,Default,,0000,0000,0000,,So if you say how many times 13 goes into\N120?
Dialogue: 0,0:02:42.56,0:02:48.36,Default,,0000,0000,0000,,It looks like it's like 9 times, yeah, it\Nwould go into it 9 times.
Dialogue: 0,0:02:48.36,0:02:52.46,Default,,0000,0000,0000,,9 times, 9 times 3, get rid of this, 3\Ntimes 3 is 27.
Dialogue: 0,0:02:52.46,0:02:58.95,Default,,0000,0000,0000,,9 times 1 is 9, plus 2 is 11, you have a\Nremainder of 3.
Dialogue: 0,0:02:58.95,0:03:04.90,Default,,0000,0000,0000,,So you get, it's about .69, so 6, so 6.7\Npoint would be a pretty good guess.
Dialogue: 0,0:03:04.90,0:03:08.78,Default,,0000,0000,0000,,This is .69 of the way between 36 and 49.
Dialogue: 0,0:03:08.78,0:03:13.75,Default,,0000,0000,0000,,So lets go roughly .69 of the way between\N6 and 7.
Dialogue: 0,0:03:13.75,0:03:15.23,Default,,0000,0000,0000,,So this is once again, just a approximate,
Dialogue: 0,0:03:15.23,0:03:16.80,Default,,0000,0000,0000,,it's not necessarily give us the exact\Nanswer, we
Dialogue: 0,0:03:16.80,0:03:21.44,Default,,0000,0000,0000,,have to use that as to make a good initial\Nguess and see how well it works.
Dialogue: 0,0:03:21.44,0:03:25.61,Default,,0000,0000,0000,,So lets try, lets try, 6.7.
Dialogue: 0,0:03:25.61,0:03:30.66,Default,,0000,0000,0000,,Let's try 6.7 and the really way to try it\Nis to square 6.7.
Dialogue: 0,0:03:30.66,0:03:36.47,Default,,0000,0000,0000,,So 6.7, 6.7 times 6 point, maybe I'll\Nwrite the multiplication symbol there.
Dialogue: 0,0:03:38.40,0:03:40.03,Default,,0000,0000,0000,,6.7 times 6.7.
Dialogue: 0,0:03:40.03,0:03:42.20,Default,,0000,0000,0000,,So we have 7 times 7 is 49.
Dialogue: 0,0:03:42.20,0:03:47.89,Default,,0000,0000,0000,,7 times 6 is 42, plus 4, is 46, so the 0\Nnow, cause
Dialogue: 0,0:03:49.13,0:03:54.50,Default,,0000,0000,0000,,we're now in, we're now moved up, to,\Nwe've moved a space to the left,
Dialogue: 0,0:03:54.50,0:03:59.43,Default,,0000,0000,0000,,so now we have 6 times 7 is 42, Carry the\N4.
Dialogue: 0,0:03:59.43,0:04:02.48,Default,,0000,0000,0000,,6 times 6 is 36, plus 4 is 40.
Dialogue: 0,0:04:02.48,0:04:06.13,Default,,0000,0000,0000,,And so 9 plus 0 is 9, 6 plus 2 is 8, 4
Dialogue: 0,0:04:06.13,0:04:10.58,Default,,0000,0000,0000,,plus 0 is 4, and then we have a 4 right\Nover here.
Dialogue: 0,0:04:10.58,0:04:14.04,Default,,0000,0000,0000,,And we have two total numbers behind the\Ndecimal point, one, two.
Dialogue: 0,0:04:14.04,0:04:16.67,Default,,0000,0000,0000,,So this gives us 44.89.
Dialogue: 0,0:04:16.67,0:04:19.61,Default,,0000,0000,0000,,So 6.7 gets us pretty close, but we're\Nstill
Dialogue: 0,0:04:19.61,0:04:22.19,Default,,0000,0000,0000,,not, we're still not probably right to the\Nhundreds,
Dialogue: 0,0:04:22.19,0:04:23.94,Default,,0000,0000,0000,,well, it's definitely not to the hundreds\Nplace since
Dialogue: 0,0:04:23.94,0:04:26.88,Default,,0000,0000,0000,,we've only gone To the tenth place right\Nover here.
Dialogue: 0,0:04:26.88,0:04:30.47,Default,,0000,0000,0000,,So if we want to get to 45, the, the 6.7\Nsquared is still less
Dialogue: 0,0:04:30.47,0:04:35.14,Default,,0000,0000,0000,,than, the square root, or I should say,\N6.7 squared is still less than 45.
Dialogue: 0,0:04:35.14,0:04:38.70,Default,,0000,0000,0000,,Or 6.7 is still less than the square root\Nof 45.
Dialogue: 0,0:04:38.70,0:04:42.15,Default,,0000,0000,0000,,So, let's try 6.71.
Dialogue: 0,0:04:42.15,0:04:44.69,Default,,0000,0000,0000,,So let's try 6 point, let me do this in a\Nnew color.
Dialogue: 0,0:04:45.84,0:04:47.92,Default,,0000,0000,0000,,I'll do 6.71 in pink.
Dialogue: 0,0:04:47.92,0:04:49.00,Default,,0000,0000,0000,,So let's try 6.7.
Dialogue: 0,0:04:49.00,0:04:50.52,Default,,0000,0000,0000,,We'll increase it a little bit.
Dialogue: 0,0:04:50.52,0:04:54.99,Default,,0000,0000,0000,,See if we can go from 44.89 to 45, cuz\Nthis is really close already.
Dialogue: 0,0:04:54.99,0:04:55.61,Default,,0000,0000,0000,,And if this is.
Dialogue: 0,0:04:55.61,0:04:56.96,Default,,0000,0000,0000,,Well let's just try it out.
Dialogue: 0,0:04:56.96,0:04:57.18,Default,,0000,0000,0000,,6.71.
Dialogue: 0,0:04:57.18,0:05:01.99,Default,,0000,0000,0000,,So once again, we have to do some\Narithmetic by hand.
Dialogue: 0,0:05:01.99,0:05:04.82,Default,,0000,0000,0000,,We are assuming that they don't want us to\Nuse a calculator here.
Dialogue: 0,0:05:04.82,0:05:09.72,Default,,0000,0000,0000,,So if 1 times 1 is 1, 1 times 7 is 7, 1\Ntimes 6 is 6.
Dialogue: 0,0:05:09.72,0:05:16.60,Default,,0000,0000,0000,,A 0 here, 7 times 1 is 7, 7 times 7 is 49,\N7 times 6 is 42, plus 4 is 46.
Dialogue: 0,0:05:16.60,0:05:24.61,Default,,0000,0000,0000,,And then we have two zeros here, 6 times 1\Nis 6, 6 times 7 is 42.
Dialogue: 0,0:05:24.61,0:05:33.32,Default,,0000,0000,0000,,Used to have this new four new, 6 times 6,\N6 times 6 is 36, plus 4 is 40.
Dialogue: 0,0:05:33.32,0:05:33.88,Default,,0000,0000,0000,,Plus 480.
Dialogue: 0,0:05:33.88,0:05:37.87,Default,,0000,0000,0000,,So if you really, well, it's interesting\Nto think
Dialogue: 0,0:05:37.87,0:05:40.64,Default,,0000,0000,0000,,what we got incrementally by adding that,\Nthat one
Dialogue: 0,0:05:40.64,0:05:43.82,Default,,0000,0000,0000,,hundredth over there because this part\Nover here, well,
Dialogue: 0,0:05:43.82,0:05:45.48,Default,,0000,0000,0000,,we'll see, actually, when we add all this\Nup.
Dialogue: 0,0:05:45.48,0:05:47.01,Default,,0000,0000,0000,,You get a 1.
Dialogue: 0,0:05:47.01,0:05:49.13,Default,,0000,0000,0000,,7 plus 7 is 14.
Dialogue: 0,0:05:49.13,0:05:53.93,Default,,0000,0000,0000,,1 plus 6 plus 9 is 16, plus 6.
Dialogue: 0,0:05:53.93,0:05:54.16,Default,,0000,0000,0000,,Is 22.
Dialogue: 0,0:05:54.16,0:05:58.48,Default,,0000,0000,0000,,2 plus 6 plus 2 is 10.
Dialogue: 0,0:05:58.48,0:06:04.52,Default,,0000,0000,0000,,And then 1 plus 4 is 5 and then we bring\Ndown the 4.
Dialogue: 0,0:06:04.52,0:06:11.34,Default,,0000,0000,0000,,And we have 1, 2, 3, 4 numbers behind the\Ndecimal point.
Dialogue: 0,0:06:11.34,0:06:12.32,Default,,0000,0000,0000,,1, 2, 3, 4.
Dialogue: 0,0:06:12.32,0:06:17.66,Default,,0000,0000,0000,,So when we squared 6.71, 6.71 is equal to\N45.02.
Dialogue: 0,0:06:17.66,0:06:22.58,Default,,0000,0000,0000,,41, so 6.71 is a little bit greater.
Dialogue: 0,0:06:22.58,0:06:24.33,Default,,0000,0000,0000,,So let's, let me make it clear now.
Dialogue: 0,0:06:24.33,0:06:31.97,Default,,0000,0000,0000,,We know that, 6.7 is less than the square\Nroot of 45, and we know that, that is less
Dialogue: 0,0:06:31.97,0:06:35.45,Default,,0000,0000,0000,,than 6.71 cause when we square this we get
Dialogue: 0,0:06:35.45,0:06:38.34,Default,,0000,0000,0000,,something a little bit over the square\Nroot of 45.
Dialogue: 0,0:06:38.34,0:06:40.78,Default,,0000,0000,0000,,But he key here is, is when we square
Dialogue: 0,0:06:40.78,0:06:46.40,Default,,0000,0000,0000,,this, so 6.7 squared, so let's, 6.7\Nsquared guys.
Dialogue: 0,0:06:46.40,0:06:53.70,Default,,0000,0000,0000,,44.89 which is eleven hundredths, eleven\Nhundredths away from 45.
Dialogue: 0,0:06:53.70,0:06:58.52,Default,,0000,0000,0000,,So, this is and then if we look at 6.71\Nsquared, we're only
Dialogue: 0,0:06:58.52,0:07:05.98,Default,,0000,0000,0000,,2.400ths above 45, so this right here is\Ncloser to the square root of 45.
Dialogue: 0,0:07:05.98,0:07:11.21,Default,,0000,0000,0000,,So if we approximate, to the hundreths\Nplace, definitely want to go with 6.7.