Surds / Radicals - the basics - adding and subtracting made easy - Free Educational videos for Students in K-12

Surds / Radicals - the basics - adding and subtracting made easy - By tecmath

Transcript


00:0-1	Good day and welcome to the tech Math channel .
00:01	What we're gonna be having a look at this video
00:03	is going to be looking at how to add and
00:05	subtract surge . So this looks this , this takes
00:09	into account a few of the ideas that we've looked
00:12	at in previous videos , looking at sides and first
00:15	off , I'll go through a couple of these .
00:16	First off would assert actually was now the third is
00:18	a number which is exactly expressed as say something under
00:22	a square root side . Okay , so the square
00:24	root of two . Now we wanna type this in
00:26	the calculator , you get this number with a big
00:28	long string of decimal places after that are never occurring
00:31	. So the most accurate way of saying expressing this
00:34	answer this number is As the square root of two
00:39	. Um , the other things we looked at ,
00:41	the other videos was Hannah multiple suits where we ,
00:44	we found this particular law or rule which was the
00:48	square root of a . Times the square root of
00:52	B is equal to the square root of a ,
00:57	times B . Now , an example of this is
01:00	a square two times the square root of three is
01:03	equal to the square root of two times three ,
01:05	which is the square root of six . Another really
01:08	, really important property to understand is that we have
01:12	to look at what searches can be simplified by expressing
01:15	the number under the root sign . Um is a
01:17	product of factors . So one of these factors you're
01:20	looking for is a perfect square . So one of
01:22	the factors of the numbers under here is a perfect
01:24	square . It means that you can simplify it a
01:27	little bit further to say you had the square root
01:30	of 12 . Well you can actually one of the
01:33	factors before you can actually simplify that a little bit
01:35	further . Okay , if you can't , you can't
01:38	absolutely simplify further . So we're gonna be having a
01:40	look at this today . Well in this video ,
01:43	so let's have a look at a couple of examples
01:46	to start us off with this uh perfect squares .
01:48	By the way , we might be looking to say
01:49	something like two squared , which is four or three
01:53	squared , which is nine or 4 squared , which
01:57	is 16 Five squared , 25 and so on and
02:01	so forth . So I might even keep those up
02:05	for when we're working through these because it's a really
02:07	great idea to get , it's one of the big
02:09	ideas to get is how you can actually simplify them
02:11	further and we did look at that , but I
02:13	think it's it's something which eludes people a little bit
02:15	. So um with much further talking , I'm just
02:20	gonna launch into how to add and subtract . So
02:22	it's now say you can't say something like four times
02:26	square at a two . And we want to add
02:29	this to five times the square in it too .
02:33	Now we can do this . And the reason for
02:35	this is as follows , this is equal here for
02:40	Times Square at a two and this one over here
02:43	is equal to five times a swimming too . Okay
02:47	so all together we have square into two . We
02:51	actually have altogether This many plus this money . So
02:55	we actually altogether have nine time to swear or two
02:59	and just write this nine square root two . So
03:01	this is the answer to this . So you can
03:03	directly add searches together like this . As long as
03:07	you have these like terms as I said , okay
03:11	just square it three . You couldn't add these guys
03:13	but as long as there's a like terms you can
03:16	add the . Okay now um let's take this a
03:20	little bit further . So say for example , we
03:23	wish to do something like the following . We wish
03:26	to say um do something like three times the square
03:32	root of three . And I want to add this
03:35	to two times the square root of six as add
03:40	this to the square root of three . Now look
03:46	if you can say something like this to answer what
03:49	you might notice straightaway is that we have a life
03:52	term here to here . Okay , so we can
03:55	add these guys together . We get this answer of
03:58	three square at three plus square root three . Cool
04:02	square roots . Right this number here . They can't
04:05	be simplified any further because it has no factors that
04:09	are perfect squares . Actually none of these do .
04:11	So it can't be simplified any further and it is
04:13	an unlocked term . So we just have to actually
04:15	write this as two square at six and that's how
04:18	we know when we finish these questions . We should
04:21	be able to look at each of the actual numbers
04:23	under the square root sign and go , well ,
04:25	they've got no factors that are actually perfect squares here
04:28	. Okay , so it's a really important thing to
04:30	get . So this year is our answer . Okay
04:36	, so what about we add something a little bit
04:39	harder now ? So say I get you to add
04:44	Um we'll add it together the square root of eight
04:50	Plus the Square Root of 18 . Now , this
04:55	can be simplified a bit further because if we have
04:58	a look at the square of the factors of we
05:01	have a couple that are actually perfect squares , We
05:03	actually have one , that's a perfect square , which
05:05	is four . Okay , so this one here is
05:07	equal to the square root oh , four times two
05:14	. Okay . Which is we can break up further
05:16	because there's this law when we multiply them into the
05:19	square root of form and the square root of two
05:27	. Okay , We're adding this to the square in
05:30	19 . So this here can also be broken up
05:33	into the square root . And if you have a
05:35	look here because we have nine , nine times two
05:39	, Which can again be broken up into the square
05:41	at nine Time to Square at two . Okay ,
05:46	these are being added together . Okay , So we
05:50	can go through an answer a couple of these because
05:52	the swearing of four is too and the square root
05:55	of nine is 3 and this is being multiplied by
05:58	the square or two . So I can just write
05:59	the square or two next to it . And this
06:01	is being multiplied by the square or two . We're
06:03	adding these guys together . So what we end up
06:06	with is three square root soup two square inches ,
06:09	sorry , and three plus three squared to five square
06:14	. Again , this has no factors obviously that there's
06:17	no factors apart in two months , we can't take
06:19	this any further . This is area itself . So
06:22	hopefully your understanding that hopefully this is really beginning to
06:27	get how you can actually even see an answer when
06:30	you've got one of these . Okay , because it
06:31	is a real art form , I think doing so
06:34	I've got very confused . I remember at school doing
06:36	these Because I didn't quite understand that . So I'm
06:39	gonna get through one last example , what a way
06:41	to do . The square root of 54 plus The
06:46	square root of 45 Plus the Square Root of 125
06:54	. Now with these Look for factors that are perfect
06:57	squares and see if we can simplify them this fall
07:01	, going to them , there's nine and you're looking
07:03	for possibly the biggest ones if you can . So
07:05	nine Goes into 54 . He goes in , No
07:10	one goes in the square root of nine and we
07:14	have the square root of six . Okay , because
07:19	6 , 1954 over here , we're the ones we're
07:23	going to be adding the pluses are different signs .
07:26	We can really separate things up here . So over
07:29	here we have 45 and 45 . The numbers that
07:31	go into it here . 9545 . So we have
07:36	the square root of norman Times the square root of
07:40	five we're adding this to . Finally , We have
07:46	a look here . The numbers are going here .
07:48	The largest one I can think of the year is
07:49	25 , 20 . The score of 25 and 25
07:53	times Five some of the square root of 525 .
07:59	How are you ? Good with that ? So we
08:00	can answer a couple of these . two square to
08:02	nine is 3 . The square tonight here is three
08:05	and the square of the 25 is five . And
08:08	then we just write these square , it's next .
08:10	So square of six . The square root of five
08:14	. The square root of five . Because that's why
08:16	multiple into one . We put the same signs between
08:21	. So do we have any life terms here ?
08:22	We do . So we can add these guys together
08:24	. We end up with three so that the Eagles
08:29	three times the square to five plus 52 square at
08:32	five . So I put this one down here first
08:35	actually because it's a small town that order this is
08:38	going to be three times square the sixties or by
08:40	himself . He can't be uh factories anymore . None
08:43	of these numbers here going to none of these perfect
08:45	square numbers go into it . So he can't join
08:47	you any further down . And these guys here ,
08:49	they're they're factors can't go any further down because there
08:51	that could be they don't have any factors that are
08:53	prolific squares in them . So we just have to
08:55	add these guys together . So three plus 58 square
08:59	root five . And that's our answer . So hopefully
09:02	that really helped you adding the adding square root numbers
09:07	. Um and subtracting , look , I know I
09:09	didn't actually do an example there , but subtracting a
09:11	similar sort of thing just where you would actually be
09:13	taking numbers away obviously . But really really important .
09:16	I think that you understand how to multiply searches .
09:19	But also um and that that that's in order to
09:23	add them . But also that this idea of how
09:25	you can factories and using this idea of a perfect
09:28	square numbers . Perfect square factor . Okay . I
09:31	hope that was a big help . Um , good
09:34	luck in doing searches in math class . See you
09:36	next time .

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