Simplifying Square Roots - Free Educational videos for Students in K-12

Simplifying Square Roots - By tecmath

Transcript


00:0-1	get a welcome to take Math channel . What we're
00:02	going to be having a look at this video is
00:04	going to be looking at how to simplify certain now
00:07	. Uh look , I know a couple of things
00:09	. First off sides and not everybody's favorite mathematical topic
00:14	. In fact , I remember at school actually really
00:16	hated doing certain . Uh so I'm going to try
00:19	and make this as simple as possible . Okay ,
00:21	because I remember being actually utterly confused at school with
00:24	these um yeah , that expression simplifying always thought would
00:28	be a strange expression , always gonna be a lot
00:30	more simple if you are didn't do this sort of
00:32	thing , but here you go . Um first off
00:35	thirds numbers which basically can only be expressed exactly using
00:41	A root power . So say the square root of
00:45	two . If you were to type this into your
00:46	calculator , this would be give you an answer to
00:49	say , 1.414 and I will give you a whole
00:52	string of decimals . But the thing is these decimals
00:55	would never hit a pattern . They'd never become recurring
00:58	. There'd just be this seemingly random string of decimals
01:03	and they'd never end . So this thing is known
01:05	as a rational number and this is the reason we
01:07	use surges because this is the most exact way we
01:10	can express this particular value . Okay , so uh
01:14	we're gonna be looking at simplifying so it's bigger ones
01:17	in this now . The way that we basically do
01:20	this is using the information that we have of how
01:23	to multiply surge when we multiply circuits we have this
01:26	rule . Now I'm gonna throw this particular rule that
01:29	you and I'm going to explain it once again .
01:31	So you know how it works . Okay . So
01:33	if you haven't seen any earlier videos and how to
01:35	multiply sir , that's okay . You'll be able to
01:37	catch up here . So the rule for multiplying surges
01:41	as follows , where we have the square root of
01:44	an expression A times the square root of some number
01:48	B equals the square root of A times B .
01:53	Now that's a nice , simple sort of thing .
01:55	I'll explain how this works using non certain numbers .
01:58	So so we have the square root of four and
02:02	with times this by the square root of nine .
02:05	Now the square root of four is two and the
02:07	square root of nine is three . We multiply these
02:11	. We had six , right ? Because that's where
02:13	the four is two and square in 93 . We
02:15	multiply these . We had six . This is equal
02:18	to or six is the square root of 36 .
02:23	You can see it's four times nine is 36 .
02:25	And this is this rule does work here . Okay
02:28	, so hopefully you're pretty comfortable with this rule .
02:30	Okay , so you get comfortable with and we'll use
02:35	it to actually simplify a few Third expressions . Okay
02:41	, so the first ones we're going to do these
02:43	um we'll do three of them . We do say
02:46	the square root of 28 . Yeah . What we
02:51	used to do these is we use uh numbers that
02:56	are going to help us get a perfect square .
02:58	I'll show you this what I mean by this .
03:00	So say it's really worth actually when you do this
03:04	, joining down a quick list . So we have
03:06	two squared which is four , we have three squared
03:10	, which is nine , we have four squared ,
03:13	which is 16 , we have five squared , which
03:16	is 25 . We have six squared , which is
03:19	36 7 squared , 49 so on and so forth
03:24	. We're going to use these to help us simplifies
03:27	. We're going to use this rule and this idea
03:30	here to help us simplify these expressions . And when
03:34	we when you're getting asked in math to try and
03:36	simplify this , what they're literally asking you to do
03:38	is they're trying to get you to get the lowest
03:42	possible surgery can here and there might be some number
03:44	of times just lowest possible number here . Okay ,
03:47	now the way we do this is as follows ,
03:49	I'll show you the steps in doing this . So
03:51	, first of what we want to do here is
03:54	We literally look for some factors of 28 , especially
03:58	ones where we have One of these numbers here ,
04:03	there's 4 9 , 16 right now Here we have
04:06	28 and 28 . The number four goes into it
04:09	. So four goes into it and 47 28 .
04:14	So what we have here Is 28 is equal to
04:18	the square root of four times The square root of
04:22	seven . Because this particular rule here says that's the
04:26	case , I hope you're good with that . So
04:29	we can simplify this further because the square root of
04:32	four is too , And we're gonna be times ,
04:34	you know , by the square root of seven .
04:37	Now , does that look simpler at all ? Hey
04:39	look , it doesn't look that much simpler than they
04:41	always grant that , but that is what you're being
04:43	asked to when you're being asked to simplify these .
04:45	Okay , so hopefully you're pretty good with these ,
04:49	let's give another one in practice . Okay , so
04:52	You should be pretty good with these . Okay ,
04:54	it does take a bit of the guesswork out once
04:56	you know what you're doing with obviously now , uh
05:00	just say we're going to get you to work out
05:02	the square root of 72 . Then you ask to
05:06	simplify this Now , Just one thing with this .
05:09	So you decided , you know what I'm gonna do
05:11	is find some factors of 72 And you might look
05:14	down your list here and think , Okay , there's
05:15	four going to 72 and you'll find out what it
05:18	does . There's no I'm going to 72 and you'll
05:22	find that it does to 16 Go into 72 .
05:27	No , 25 dozen . But $36 , goes in
05:31	twice . 49 dozen . So we have three different
05:35	uh numbers here that actually go into 72 . The
05:39	perfect square . So we can have 49 or 36
05:43	here . The one that you choose is the largest
05:46	ones at 36 . Okay , so this one equals
05:49	the square root of 36 Times The Square Root of
05:55	two . Okay , because this will give us the
05:59	lowest possible . Certainly does that make sense . So
06:02	if we simplify this square at 36 is six .
06:07	We're gonna be multiplying that by the square of the
06:09	two . And again , that's the most simple expression
06:13	you can get for this . So what about we
06:15	give you ? I'll give you one more example for
06:17	this . Okay , Because this I remember , I'll
06:22	be honest , I went a holy way at school
06:25	in this , I think I remember . Okay ,
06:28	so let's go through another example here . So I
06:33	say I want you to actually go through and find
06:37	a simplification . In fact , I'm gonna go through
06:39	a couple more examples . The square root of What
06:44	about we do 48 . So it's worth going through
06:49	your list here and you go , well for goes
06:51	into it . Um What else goes into it here
06:54	. Does not go into it . Nine doesn't go
06:56	into it , just 16 . Go into it .
06:58	Uh Yeah , it does Goes in three times .
07:01	Yeah , 25,036,049 dozen . So these are two numbers
07:07	here , So we're gonna make this , this is
07:11	the one we're going to choose here . The 16
07:13	, so this is equal to the square root of
07:16	16 , and the number of times was 16 to
07:18	get 48 is three . Okay , so Let's work
07:29	this out . So square 16 , is this so
07:33	the squares 16 is full , and we're gonna put
07:38	that Times Square to three , and that's how simplified
07:42	answer . So hopefully you're pretty good with this now
07:45	, I'm gonna just give you a slight variation that
07:47	you might get on these . Okay , I just
07:50	would think it would be a bit remiss of me
07:52	if I didn't do this . Okay , so You
07:56	might also get these sort of things where you actually
07:58	to use , you get asked to actually uh say
08:01	work out the simplification to say something like this .
08:04	five square root , 12 , So what are you
08:09	doing this Again , treat this is much the same
08:12	at the start and we have to find some factors
08:14	at 12 , so four goes into it , and
08:17	four was going to be a factor here . Okay
08:19	, so we don't have We're gonna have four and
08:23	three here , so this is equal to five times
08:26	the square root of full times the square root of
08:32	three . Okay , I probably could have written that
08:35	a little bit nicer actually . In fact , I
08:37	might Okay , so five times the square root of
08:44	four times the square root of three . Okay ,
08:48	so all you've really done is just put this fire
08:50	out the front . Okay , so if we would
08:53	do this , This is equal to five times square
08:57	at four , which is to Time to swear at
09:00	three and this week is actually taking it further .
09:03	So it's five times to his tent . Uh huh
09:07	. With multiple this square and three . So there's
09:09	our answer . So how do you feel with those
09:12	? Do you feel ok with him ? Hopefully you
09:14	feel really good with simplifying surgeons . They're not that
09:16	bad . Okay . Look , I'll agree with you
09:20	. They don't ever to me and I feel like
09:22	I'm quite an answer . Okay . This to me
09:24	feels like a problem unto itself , but this is
09:26	what you're being asked doing . That's when you're being
09:28	asked . So hopefully that's made a little bit easier
09:31	anyway . Thanks for watching . We'll see you next
09:33	time . Bye .

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