[Script Info]
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Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.50,0:00:09.06,Default,,0000,0000,0000,,Let's see if we can simplify 5\Ntimes the square root of 117.
Dialogue: 0,0:00:09.06,0:00:13.06,Default,,0000,0000,0000,,So 117 doesn't jump out at me as\Nsome type of a perfect square.
Dialogue: 0,0:00:13.06,0:00:14.99,Default,,0000,0000,0000,,So let's actually take\Nits prime factorization
Dialogue: 0,0:00:14.99,0:00:20.13,Default,,0000,0000,0000,,and see if any of those prime\Nfactors show up more than once.
Dialogue: 0,0:00:20.13,0:00:21.75,Default,,0000,0000,0000,,So clearly it's an odd number.
Dialogue: 0,0:00:21.75,0:00:24.14,Default,,0000,0000,0000,,It's clearly not divisible by 2.
Dialogue: 0,0:00:24.14,0:00:25.73,Default,,0000,0000,0000,,To test whether\Nit's divisible by 3,
Dialogue: 0,0:00:25.73,0:00:27.06,Default,,0000,0000,0000,,we can add up all of the digits.
Dialogue: 0,0:00:27.06,0:00:29.81,Default,,0000,0000,0000,,And we explain why this works in\Nanother place on Khan Academy.
Dialogue: 0,0:00:29.81,0:00:31.86,Default,,0000,0000,0000,,But if you add up all\Nthe digits, you get a 9.
Dialogue: 0,0:00:31.86,0:00:36.22,Default,,0000,0000,0000,,And 9 is divisible by 3, so 117\Nis going to be divisible by 3.
Dialogue: 0,0:00:36.22,0:00:37.60,Default,,0000,0000,0000,,Now, let's do a\Nlittle aside here
Dialogue: 0,0:00:37.60,0:00:41.34,Default,,0000,0000,0000,,to figure out what 117\Ndivided by 3 actually is.
Dialogue: 0,0:00:41.34,0:00:43.70,Default,,0000,0000,0000,,So 3 doesn't go into 1.
Dialogue: 0,0:00:43.70,0:00:46.01,Default,,0000,0000,0000,,It does go into 11, three times.
Dialogue: 0,0:00:46.01,0:00:47.67,Default,,0000,0000,0000,,3 times 3 is 9.
Dialogue: 0,0:00:47.67,0:00:50.39,Default,,0000,0000,0000,,Subtract, you got\Na remainder of 2.
Dialogue: 0,0:00:50.39,0:00:53.40,Default,,0000,0000,0000,,Bring down a 7.
Dialogue: 0,0:00:53.40,0:00:55.85,Default,,0000,0000,0000,,3 goes into 27 nine times.
Dialogue: 0,0:00:55.85,0:00:58.09,Default,,0000,0000,0000,,9 times 3 is 27.
Dialogue: 0,0:00:58.09,0:00:59.17,Default,,0000,0000,0000,,Subtract, and you're done.
Dialogue: 0,0:00:59.17,0:01:02.08,Default,,0000,0000,0000,,It goes in perfectly.
Dialogue: 0,0:01:02.08,0:01:07.55,Default,,0000,0000,0000,,So we can factor\N117 as 3 times 39.
Dialogue: 0,0:01:07.55,0:01:10.94,Default,,0000,0000,0000,,Now 39, we can factor as--\Nthat jumps out more at us
Dialogue: 0,0:01:10.94,0:01:13.01,Default,,0000,0000,0000,,that that's divisible by 3.
Dialogue: 0,0:01:13.01,0:01:15.82,Default,,0000,0000,0000,,That's equivalent to 3 times 13.
Dialogue: 0,0:01:15.82,0:01:18.32,Default,,0000,0000,0000,,And then all of these\Nare now prime numbers.
Dialogue: 0,0:01:18.32,0:01:23.58,Default,,0000,0000,0000,,So we could say that this\Nthing is the same as 5 times
Dialogue: 0,0:01:23.58,0:01:34.58,Default,,0000,0000,0000,,the square root of\N3 times 3 times 13.
Dialogue: 0,0:01:37.06,0:01:39.56,Default,,0000,0000,0000,,And this is going to be the\Nsame thing as-- and we know this
Dialogue: 0,0:01:39.56,0:01:43.21,Default,,0000,0000,0000,,from our exponent\Nproperties-- 5 times
Dialogue: 0,0:01:43.21,0:01:54.88,Default,,0000,0000,0000,,the square root of 3 times 3\Ntimes the square root of 13.
Dialogue: 0,0:01:54.88,0:01:56.74,Default,,0000,0000,0000,,Now, what's the square\Nroot of 3 times 3?
Dialogue: 0,0:01:56.74,0:01:58.16,Default,,0000,0000,0000,,Well, that's the\Nsquare root of 9.
Dialogue: 0,0:01:58.16,0:01:59.73,Default,,0000,0000,0000,,That's the square\Nroot of 3 squared.
Dialogue: 0,0:01:59.73,0:02:02.12,Default,,0000,0000,0000,,Any of those-- well, that's\Njust going to give you 3.
Dialogue: 0,0:02:02.12,0:02:04.59,Default,,0000,0000,0000,,So this is just going\Nto simplify to 3.
Dialogue: 0,0:02:04.59,0:02:10.47,Default,,0000,0000,0000,,So this whole thing is 5 times\N3 times the square root of 13.
Dialogue: 0,0:02:10.47,0:02:14.75,Default,,0000,0000,0000,,So this part right over\Nhere would give us 15 times
Dialogue: 0,0:02:14.75,0:02:19.85,Default,,0000,0000,0000,,the square root of 13.
Dialogue: 0,0:02:19.85,0:02:21.75,Default,,0000,0000,0000,,Let's do one more example here.
Dialogue: 0,0:02:21.75,0:02:29.90,Default,,0000,0000,0000,,So let's try to simplify 3\Ntimes the square root of 26.
Dialogue: 0,0:02:29.90,0:02:31.77,Default,,0000,0000,0000,,I'm actually going\Nto put 26 in yellow,
Dialogue: 0,0:02:31.77,0:02:35.16,Default,,0000,0000,0000,,like I did in the\Nprevious problem.
Dialogue: 0,0:02:35.16,0:02:37.44,Default,,0000,0000,0000,,Well, 26 is clearly\Nan even number,
Dialogue: 0,0:02:37.44,0:02:38.90,Default,,0000,0000,0000,,so it's going to\Nbe divisible by 2.
Dialogue: 0,0:02:38.90,0:02:41.92,Default,,0000,0000,0000,,We can rewrite it as 2 times 13.
Dialogue: 0,0:02:41.92,0:02:42.75,Default,,0000,0000,0000,,And then we're done.
Dialogue: 0,0:02:42.75,0:02:43.82,Default,,0000,0000,0000,,13 is a prime number.
Dialogue: 0,0:02:43.82,0:02:45.86,Default,,0000,0000,0000,,We can't factor this any more.
Dialogue: 0,0:02:45.86,0:02:48.20,Default,,0000,0000,0000,,And so 26 doesn't have\Nany perfect squares in it.
Dialogue: 0,0:02:48.20,0:02:49.62,Default,,0000,0000,0000,,It's not like we\Ncan factor it out
Dialogue: 0,0:02:49.62,0:02:50.97,Default,,0000,0000,0000,,as a factor of\Nsome other numbers
Dialogue: 0,0:02:50.97,0:02:52.72,Default,,0000,0000,0000,,and some perfect squares\Nlike we did here.
Dialogue: 0,0:02:52.72,0:02:55.43,Default,,0000,0000,0000,,117 is 13 times 9.
Dialogue: 0,0:02:55.43,0:02:58.74,Default,,0000,0000,0000,,It's the product of a\Nperfect square and 13.
Dialogue: 0,0:02:58.74,0:03:01.64,Default,,0000,0000,0000,,26 isn't, so we've simplified\Nthis about as much as we can.
Dialogue: 0,0:03:01.64,0:03:08.14,Default,,0000,0000,0000,,We would just leave this as 3\Ntimes the square root of 26.