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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