Surds / Radicals - the basics made easy with radical math - Free Educational videos for Students in K-12

Surds / Radicals - the basics made easy with radical math - By tecmath

Transcript


00:00	good day and welcome to the technical channel . What
00:02	we're gonna be having a look at in this video
00:04	is this is gonna be the last of the sort
00:06	of the combination of looking at search ads where we're
00:09	looking at basically how to do some more complex operations
00:14	with them . Now . Now we've looked at multiplying
00:16	and dividing cells , we looked at addition absurd .
00:18	We also looked at simplifying and so those videos are
00:21	probably really , really good if you haven't seen them
00:24	yet . But basically what they showed were a couple
00:26	of things . First off sides , what they are
00:28	there a type of number which is generally expressed as
00:32	a root of another thing ? Number , a root
00:34	of a number . So say something like square at
00:36	two of the square root of three . Um Now
00:39	we've worked out that serves in the in the multiplication
00:43	, we worked out inserts could be multiplied . So
00:45	say something like the square root of a times square
00:49	, it would be was equal to the square of
00:52	a times B stand square did say three times the
00:55	square root of uh two is like the square root
00:59	of six . Okay , A simple thing of saying
01:01	or divided , which is a very vice versa .
01:04	I think of those . I'm not gonna write that
01:06	particular rule down . We also found out the terms
01:09	that had the same sir could be added us attracted
01:11	. I'll give you an example this . So um
01:13	, so say If something was like the Square three
01:17	times the square root of a plus four times a
01:21	squared of hey , we end up with say seven
01:25	times square . And so these could be directly added
01:28	like this . We also found that we could actually
01:30	simplify certain sides . Um , if the number under
01:36	the square root sign had a factor which was a
01:38	perfect square in a perfect square would say something like
01:41	um were two squared equals four or three squared equals
01:47	nine . So if you can go through those previous
01:49	videos and get those or if you understand that already
01:51	, you'll be fine for this next thing we're going
01:53	to talk about . So if you have , if
01:57	you're gonna struggle with those , I recommend you can
01:59	happen . So let's have a bit of a look
02:02	at the type of questions and we're looking at in
02:04	this . Okay , so this is this type of
02:06	questions too . So you got to say something like
02:08	uh the square root of five , and we're gonna
02:12	be multiplying this by um something in brackets here two
02:17	plus two squared of three . Okay , This is
02:20	nice and simple to start off now , the way
02:23	that we do this is as follows . Now this
02:27	is fairly simple . We're just gonna multiply this number
02:31	by this number and this number , this number .
02:33	It's just a matter of expanding the bracket . So
02:35	we're gonna start out doing a fairly basic ones of
02:37	these , and then we're gonna get to more complex
02:39	ones , so this is equal to The square to
02:44	five times two . Okay , this one's here ,
02:50	and we're going to add this to the square and
02:52	a five , Which is time to buy the square
02:56	or three . Okay . And so we can actually
03:00	then take us a little bit further and to times
03:02	square to five , two square root fires uh Three
03:09	times a squared uh squared at five times the square
03:13	root of three . Well , that was equal to
03:15	that when you multiply serves , this is equal to
03:18	the square root of 15 . Okay , We can't
03:22	simplify this any further . So , this is our
03:24	answer . I know once again with thirds , it
03:27	sometimes doesn't feel like you've actually got an answer .
03:29	This is our answer here . Okay , because we
03:31	can't actually get this down to factors which are going
03:34	to work really nicely over here as well , so
03:36	. Okay , that's that's that's what it is or
03:39	what ? Yeah , let's have a and look at
03:43	a harder type of question here . So what about
03:48	we do this particular one here ? Um Say we
03:53	do oh uh so we had this one here ,
03:59	the square 23 and we're gonna time just by two
04:07	plus the square of the three . Okay , so
04:10	if we were doing this the way we do this
04:13	as follows , so again we just multiply um we're
04:16	going to expand these brackets out and then try to
04:18	simplify it . Okay , so first we're gonna multiply
04:20	these two terms and then we're gonna multiply these two
04:23	. Okay , so we're going to have first off
04:26	the square 23 times two , And we're gonna be
04:30	adding that to the square root of three times the
04:34	square root of three . Now you might think well
04:36	the square to three times the square root of three
04:38	is actually gonna be three . Okay , so our
04:42	answer here is going to be two times the square
04:45	root of three plus three . Okay , I want
04:51	to give you one more example with these . Okay
04:53	, these are these aren't too bad , but they
04:55	just take a little while to get used to .
04:57	So I say we do um seven Times The Square
05:02	Root of two . And we're going to multiply that
05:05	by the square of the six . This is in
05:09	brackets take away the square or three . Okay ,
05:12	nice and nasty looking one here . So when we
05:17	do this we get as follows , we're gonna go
05:19	uh seven times The Square of the two . And
05:24	we first off we're gonna multiply this by This number
05:27	here . Which is why this set by the Square
05:29	of six . And this is taking away seven times
05:34	the square root of two . And we're modifying this
05:39	. Bye . That's three . Okay . So this
05:45	is what we're stuck with so far . So can
05:48	we take this any further ? Well we can Now
05:51	the way we do this is as follows . So
05:53	we what we do now is we're gonna multiply these
05:55	guys , we're gonna end up with seven . And
05:59	we can multiply these guys straight through . So this
06:01	one time just one is seven square root 12 .
06:04	And this is gonna be taking away seven times the
06:09	square root and multiply these ones have six . Okay
06:12	, because when you multiply , we get that sort
06:13	of answer . So what do we get now ?
06:15	Well , you might remember that this perfect square idea
06:19	. This one doesn't have any factors that go into
06:21	this one does . This one has four and three
06:24	. This we can actually take even further and we
06:26	can say this is equal to seven times the square
06:31	root . The four times 3 Take away seven times
06:37	the square root of six . So again we can
06:40	take this a little bit further . The square root
06:42	of four is two . So this becomes uh two
06:45	years to two times seven is 14 , 14 times
06:49	the square root of three . And this is going
06:51	to be taking away seven times the square root of
06:54	six . Yeah , these are the lowest factors at
06:56	the moment . They can't go any further . So
06:59	we leave it at this . So how did you
07:01	go with that ? That was your answer there .
07:03	These are not the easiest thing . Everything . I
07:05	think people find them a little bit tricky because it's
07:08	often hard to know when to I stopped with the
07:10	things but went ahead with them . But hopefully you've
07:14	done okay with them . All right . Um Really
07:16	? What ? Hopefully that was some help with you
07:20	anyway , we'll see you next time .

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Surds / Radicals - the basics made easy with radical math is a free educational video by tecmath.

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