HK1 SQUARE ROOTS
This eighth grade mathematics lesson focuses on square numbers and square roots. It is the second in a sequence of lessons working towards Pythagoras' theorem and its applications. The lesson is taught in English and is 34 minutes in duration. There are 40 students in the class.
| Time | Caption |
|---|---|
| 00:00:06 | Okay, page 161. Uh, we have learned something about the square, do you remember? |
| 00:00:12 | No. |
| 00:00:13 | No? So uh, we have learned- for example, I give you a... question for you to think about. |
| 00:00:20 | So first of all, what is... the square... of three? |
| 00:00:30 | What is the square of three? So- so that you may understand what is the square of. |
| 00:00:36 | Six, six. |
| 00:00:39 | Six. |
| 00:00:40 | So what is the answer? |
| 00:00:41 | Six. |
| 00:00:41 | Nine. Nine. |
| 00:00:42 | Six? Yes? Uh, Leung Chi Fu. |
| 00:00:46 | Nine. |
| 00:00:47 | Nine, yes. So uh, we can answer the question like that- the square of three... is equal to nine- nine. |
| 00:00:49 | Right. [ In Chinese ] |
| 00:00:57 | So you can show the step. What is the square of nine? |
| 00:01:01 | You can use mathnotics- sorry, mathematical notation. How to write the square of three? Fung Chi Pui. |
| 00:01:08 | Three times three. |
| 00:01:09 | Three times three. And then, there is a step, the square of three. |
| 00:01:15 | So, can you write a mathematical notation? Uh, Mung Wing Chi. |
| 00:01:23 | The square. |
| 00:01:24 | The square of three? So that- can you write it on the blackboard? |
| 00:01:26 | [ Laughter ] (inaudible) |
| 00:01:29 | Are you tall enough? [ In Chinese ] |
| 00:01:30 | Are you tall enough? [ In Chinese ] |
| 00:01:31 | Wow, so long. [ In Chinese ] |
| 00:01:32 | Very big. Yes. Uh, the square of three, you can write, uh, at the same as this. |
| 00:01:38 | So that it- the meaning of uh, square of three is equal to three times three. So the answer is nine, okay? |
| 00:01:45 | So, what is the square of negative three? |
| 00:01:55 | Negative three. So can you show the step? Okay, the first- the first line, what do you- what do you write? Wong On Kei. |
| 00:02:10 | The first line. |
| 00:02:17 | Okay. So, have you found out- there's something missing. |
| 00:02:20 | So you must write down- what do you- what did you find out? What did you find? |
| 00:02:25 | Okay, uh, next. Oh, you- you can answer it again. |
| 00:02:35 | The square of... |
| 00:02:43 | Negative three. So, the square of negative three, you can write like this. And then, square means? |
| 00:02:51 | What's the- what's the meaning of square? So the answer- next step, what do you write? Ng Hoi Yan. |
| 00:03:00 | Can you answer me? |
| 00:03:01 | I want to write. |
| 00:03:03 | Okay. |
| 00:03:08 | Neg- negative three times negative three. Okay? So the answer is- what's the answer? You can answer me. |
| 00:03:18 | Uh, orally, so uh, Chan Wai Yan. |
| 00:03:21 | Nine. |
| 00:03:22 | Nine. |
| 00:03:25 | Okay, now uh, we will learn another- another type of question. |
| 00:03:54 | Okay. Now, what is the positive value of A if the square of A is nine? |
| 00:04:06 | So can you find the answers? So what is the positive value of nine? Law Oi Ping. |
| 00:04:13 | Three. |
| 00:04:14 | Three. So how can you do that? |
| 00:04:17 | How can you- how can you find the answers? |
| 00:04:19 | So first of all, you must express the square of A equals nine. So you can write an equation about A and nine. |
| 00:04:28 | So, can- what do you write on the left hand side? Wong Chun Kei. |
| 00:04:33 | A times A. |
| 00:04:35 | A times A. Or? |
| 00:04:37 | Three squared. |
| 00:04:39 | Yes, write the little two on the top. The square of A equals nine, okay? |
| 00:04:46 | So then now, we want to find A. So some of you say, the answer is three. |
| 00:04:51 | So I- I think you can go- oh three times three is nine, so the answer is three. |
| 00:04:57 | Uh, I will teach you a step to solve. So, uh, if you find the- uh, the value of A, you can write like this. |
| 00:05:04 | So A, you want to find A, then this side, you put square root, okay? So this sign- this signs... |
| 00:05:13 | We call it radical signs. Radical sign, okay? Radical sign. |
| 00:05:19 | So what is the meaning of this radical sign? So the meaning is the same as this sentence. Okay? |
| 00:05:27 | Square root of nine means to find a positive value of A, A huh, if the square of A is nine, okay? |
| 00:05:37 | Square root of nine- to find a value. |
| 00:05:41 | To find a positive value. |
| 00:05:44 | Its square equals to nine. Okay? |
| 00:05:48 | Do you know- do you understand what's the- what is the meaning of square root of a number? |
| 00:05:54 | Yes, okay. So now, number two. |
| 00:06:00 | What is the negative... value of A if the square of A is nine? |
| 00:06:15 | So the result is the same, the square of A is nine. But now, you want to find the negative number. |
| 00:06:21 | Can you find the answer? |
| 00:06:23 | Yes. |
| 00:06:29 | Yeung Suk Ping. |
| 00:06:30 | Negative three. |
| 00:06:32 | Negative three. So how can you find that? How can you find that? |
| 00:06:36 | So first of all, if the square of A is nine, then you can write an equation. |
| 00:06:42 | So, can you write an equation for me? |
| 00:06:48 | Lo Chi Hung. |
| 00:06:57 | So now, in this question, you want to find the negative value of A. |
| 00:07:01 | What is the difference? What is the difference between this part and the- and the previous question? |
| 00:07:14 | Good. [ In Chinese ] |
| 00:07:16 | But now A, A is a negative number, not negati- negative A. |
| 00:07:23 | So the square of A- the square of A is nine. Yes. |
| 00:07:29 | Haha. Is there any question? If the square of A, so which number? The square of which number? |
| 00:07:38 | [ Laughter ] |
| 00:07:48 | The square of A. You just write this sentence as a- as an equation, as an equation. |
| 00:07:50 | The square of A is [ in Chinese ] A. |
| 00:07:54 | Why? [ In Chinese ] |
| 00:07:57 | Yes, good. Okay, so A- uh, square of A equals nine. |
| 00:08:02 | So now, you will- you know that, the answer is negative three. Why? Because you- you know. |
| 00:08:11 | Because you know that, negative three times negative three equals nine. |
| 00:08:16 | So negative three squared equals nine. |
| 00:08:18 | So the answer, compared of this equation, A is negative three, okay? |
| 00:08:24 | So now, can we, uh, show the step like this? |
| 00:08:28 | So, first of all, what is the difference? So A is equal to the square root of nine. Is it the same? |
| 00:08:38 | No. |
| 00:08:39 | No, so you must add... |
| 00:08:40 | Neg- negative. |
| 00:08:41 | [ Bell ] |
| 00:08:42 | Kwong Wai Kit. |
| 00:08:46 | Yes, just- just talk. |
| 00:08:48 | Uh, a negative (inaudible) equation. |
| 00:08:49 | [ Laughter ] |
| 00:08:53 | Another sign? |
| 00:08:54 | Uh. |
| 00:08:55 | In... |
| 00:08:56 | He wants to be on camera. [ In Chinese ] |
| 00:08:57 | [ Laughter ] |
| 00:08:58 | Yes, in here. Okay? Negative sign in front of the square root. |
| 00:09:03 | So if you want to find the negative value, then in- in front of the, uh, square root- |
| 00:09:10 | Before the square root, you write a negative sign. |
| 00:09:14 | So that you can get the answer is negative three. Okay? |
| 00:09:17 | So now, I want you to find this question. So nega- square root of 36. |
| 00:09:28 | Can you find the answers? So square root of 36, what is the answer? |
| 00:09:32 | So square root of 36 means- find a number. |
| 00:09:38 | The square of this number equals 36. So which number? |
| 00:09:44 | Six. |
| 00:09:45 | Choi Ka Yan. |
| 00:09:46 | Six. |
| 00:09:47 | Six, okay? And then, negative square root of 36. So the answer is... Woo Hau Pang? |
| 00:09:55 | Negative six. |
| 00:09:56 | Negative six. Okay. |
| 00:09:59 | Open your book to page 162 to do question number two in your book. |
| 00:10:10 | Page one hundred and sixty-two, number two. |
| 00:10:22 | (inaudible) |
| 00:10:32 | (inaudible) |
| 00:11:40 | [ Laughter ] |
| 00:11:43 | (inaudible) |
| 00:12:06 | Okay. |
| 00:12:16 | Okay, part two A. Square root of 36 is six. We have done it before. Okay, part B. |
| 00:12:22 | Square root of 49. What is the answer? |
| 00:12:27 | Ng Ka Wing. |
| 00:12:28 | Seven. |
| 00:12:29 | Seven. Yes. Part C. Square root of 100. So the answer is... |
| 00:12:35 | Cheung Ka Wai. |
| 00:12:36 | Ten. |
| 00:12:38 | Ten, because 10 squared equals 100, okay? And then uh, part D. |
| 00:12:44 | Square root of 196, so the answer is...? |
| 00:12:51 | To Tsung Him. |
| 00:12:52 | Thirteen. Fourteen. |
| 00:12:54 | Fourteen. Fourteen, yes. Okay. Part E. What is the- what is the answer? |
| 00:13:01 | Wong Yee Hung- sorry, Wong Yee Ling. |
| 00:13:04 | Seventeen. Next. |
| 00:13:08 | Part F. So the answer is... Lui Man Hing? |
| 00:13:12 | Twelve. |
| 00:13:13 | Twelve. |
| 00:13:14 | No! |
| 00:13:15 | Mm? |
| 00:13:16 | Twenty. |
| 00:13:17 | Twenty. |
| 00:13:17 | [ Laughter ] |
| 00:13:18 | Twenty, yes. Okay, uh, part G, part G. So the answer is... Choi Ka Man? |
| 00:13:25 | Hmm? |
| 00:13:25 | Thirteen. |
| 00:13:26 | Thirteen, yes. Thirteen. Okay, H? The answer is...? |
| 00:13:34 | [ Laughter ] |
| 00:13:38 | Uh, Wong On Tin. |
| 00:13:39 | Nine. |
| 00:13:40 | Nine? Nineteen. Nineteen. Okay, I? What is the answer? Wong Wai Yan. |
| 00:13:47 | Chan Wai Yan. |
| 00:13:48 | [ Laughter ] |
| 00:13:48 | Negative (inaudible). |
| 00:13:49 | Huh? |
| 00:13:50 | Negative 11. |
| 00:13:51 | Negative 11. Okay, your last one. What is the answer? |
| 00:13:57 | So Chi Yan. |
| 00:14:00 | Why are you thinking about it for so long? [ In Chinese ] |
| 00:14:01 | Negative... four. |
| 00:14:04 | So you must know that, if uh, a- A squared is equal to nine, there is two- sorry, there are two answers. |
| 00:14:11 | There are two answers... to make uh, A squared equal to nine. |
| 00:14:15 | The values of A may be positive three or negative three. Why? |
| 00:14:21 | Because negative three times negative three is nine. And three times three is also equal to nine. Okay? |
| 00:14:29 | So there are two answers. |
| 00:14:31 | So if- uh, before the square root, there is uh- there is no sign, it shows it is a positive. |
| 00:14:39 | If, in front of the square root sign, there is a negative then the answer is negative. |
| 00:14:46 | Okay? Do you know- do you know how to express? |
| 00:14:50 | Okay. So now, we'll go to another... question. |
| 00:14:54 | If now, I want to find what is the value of, uh, A if the square of A is nine. |
| 00:15:03 | Now, I'm- I just want to find the values of A. I only to uh- I- I want to find the value of A. |
| 00:15:10 | Okay? But now uh- is- is there any request about A? A must be positive or negative? |
| 00:15:19 | No. So how do we wri- write this? |
| 00:15:22 | So in this case, it's similar. A squared equal to nine because it is given that the square of A is nine. |
| 00:15:30 | Next, so we know that there are- there are two answers. So how to write this? So A... |
| 00:15:38 | The- one of the answer is negative nine or...? |
| 00:15:46 | There are two answers, one of these is square root of nine. The other...? The other is...? |
| 00:15:59 | La- Lai Chi Fu. |
| 00:16:03 | Negative. [ In Chinese ] |
| 00:16:04 | Negative... square... root... |
| 00:16:09 | Square root of nine. |
| 00:16:10 | Of nine. Okay. So that means square root of nine. So you just combine the two questions, okay? |
| 00:16:16 | So before, uh, if it is positive, then it is positive square root of nine. |
| 00:16:22 | So, this is the positive square root of nine. |
| 00:16:25 | And then this one, you want to find a negative, then there is a negative. It's the same, okay? |
| 00:16:31 | So in this case, you can find the answer, this is equal to one and then this is equal to negative three. |
| 00:16:38 | So if in the question, uh, you- you want to find, uh, the value of A... |
| 00:16:44 | And then, you know A may be positive or negative, so you can express like this. |
| 00:16:50 | So there are two answers. |
| 00:16:53 | Do you have any questions? If there is no question, please do it by yourself. |
| 00:16:57 | Ah. |
| 00:16:58 | Yes, do it in your classwork. |
| 00:17:51 | Okay, find this- do these two classworks okay? Two questions. |
| 00:17:57 | So each of uh- each of the questions, you can find two answers, okay? |
| 00:18:03 | Two answers in each question. |
| 00:18:36 | (inaudible) |
| 00:18:51 | (inaudible) |
| 00:18:54 | Okay. Quick. |
| 00:19:14 | Because there are two answers. (inaudible) |
| 00:19:24 | (inaudible) |
| 00:19:25 | Did you get two answers? |
| 00:19:31 | There are two possible answers. |
| 00:19:44 | Okay, who can do this for us? Okay, number four? |
| 00:19:58 | [ Laughter ] |
| 00:19:59 | Leung Hoi Chung. |
| 00:20:04 | Number five? |
| 00:20:07 | Uh... Ng Chun Mei. |
| 00:20:25 | You're kidding. |
| 00:20:45 | (inaudible) |
| 00:20:56 | (inaudible) |
| 00:21:03 | Okay, uh, number four, so you- you write this e- equation to express this, uh, condition. |
| 00:21:10 | So the square of A equals 64. |
| 00:21:13 | So A equals the square root of 64. This is to represent a positive value, okay? |
| 00:21:18 | Or negative square root of 64. |
| 00:21:23 | So this you can find the answer is eight. This, you can get the answer negative eight. |
| 00:21:27 | So there are two answers because eight times eight is 64. |
| 00:21:33 | Negative eight times negative eight is 64. So there are two answers, okay? |
| 00:21:39 | And then, for this case, it is correct, okay? |
| 00:21:43 | In this case, you do not need to write it, uh- this sentence again- this equation again. |
| 00:21:49 | Do you have any questions? |
| 00:21:55 | Okay. There are some things for you to think about. |
| 00:22:15 | Okay. |
| 00:22:20 | [ Laughter ] |
| 00:22:26 | Okay, think... think about, uh, square root of negative four- sorry, square root of the square of negative four. |
| 00:22:35 | Is it equal to four or equal to negative four? |
| 00:22:46 | Lo Chi Hung. |
| 00:22:47 | Four. |
| 00:22:48 | Four. Why? |
| 00:22:50 | Four |
| 00:22:51 | Four. Four. |
| 00:22:53 | Negative four times negative four is- it is equal to 16 and square root of 16 is four. |
| 00:22:58 | Yes, very good. |
| 00:23:02 | Yes, very good. |
| 00:23:03 | So, this square root of the square of negative four, you can express- |
| 00:23:11 | the number inside, you can expand it as- you can calculate. |
| 00:23:15 | Negative- the square of negative four is equal to negative four times negative four. |
| 00:23:20 | So it is equal to positive 16. |
| 00:23:24 | So in this case, the answer... |
| 00:23:28 | Is it equal- equal to negative- negative four? |
| 00:23:30 | No. |
| 00:23:31 | Why? Because there is no negative sign in the front. So, the answer must be positive, okay? |
| 00:23:40 | So in this case, you can see that the answer is positive. |
| 00:23:45 | You can- you can find the answer is positive if there is no sign. Okay? |
| 00:23:51 | If the answer is negative, only if there is a negative sign, uh, before the square root, okay? |
| 00:24:02 | So in this case, there is no negative- negative sign... |
| 00:24:06 | Uh, uh, in the front, so, we call- uh, we can find the answer positive. We can find a positive answer. |
| 00:24:16 | Do you have any questions? |
| 00:24:18 | Okay. Now, uh, we have another question for- for- uh, for you to think about. Uh, it is this. |
| 00:24:48 | No solution. |
| 00:24:49 | Okay. |
| 00:24:50 | No solution. |
| 00:24:55 | Okay, wait a min- wait a minute for you to think about this. |
| 00:25:00 | So, this, uh, square root of a- sorry, uh, negative- sorry, square root of negative four. |
| 00:25:07 | Is it equal to two, or negative two, or no solution? |
| 00:25:11 | No solution, no solution. |
| 00:25:14 | Okay. Who says that it is equal to two? |
| 00:25:17 | [ Laughter ] |
| 00:25:18 | Put up your hand. |
| 00:25:22 | Why? Because take square root means- what is the number times itself equal to negative four? |
| 00:25:29 | So two times two is four. |
| 00:25:31 | So it- it does not equal negative four. It is- it does not equal negative four. |
| 00:25:36 | How about negative two? So this answer is incorrect. How about this? |
| 00:25:43 | Is it correct? |
| 00:25:44 | [ Laughter ] |
| 00:25:45 | Do you think this is correct? Please put up your hand. |
| 00:25:47 | Why? Because negative two times negative two... equals...? |
| 00:25:54 | Four. |
| 00:25:55 | Four. So it does not equal negative four. |
| 00:25:58 | So, there is...? |
| 00:26:00 | No solution. |
| 00:26:01 | No solution. |
| 00:26:02 | Why? Because, uh, if you find that it is, uh, just like that, A squared is equal to negative four. |
| 00:26:09 | So which number times itself is equal to a negative number? |
| 00:26:13 | None. |
| 00:26:14 | None. Because a number A- all number can be, uh, divided or grouped into three- uh, must be one of these. |
| 00:26:21 | One is positive. |
| 00:26:24 | One is...? |
| 00:26:25 | Negative. |
| 00:26:26 | Negative. Or... |
| 00:26:27 | No solution. |
| 00:26:29 | No solution. No. |
| 00:26:31 | A number must be one of- one of- one of these. Maybe it is a positive. Maybe it is negative, or...? |
| 00:26:40 | Zero. |
| 00:26:41 | Zero, yes. Very good. |
| 00:26:42 | So uh, if A squared- we see, uh- by case, so if A is positive, then what is the value of A squared? |
| 00:26:52 | Positive? Negative? Or zero? |
| 00:26:56 | Positive. |
| 00:26:57 | Positive. And then if it is negative, what is the result of the square of A? |
| 00:27:03 | Positive. |
| 00:27:04 | Positive. If it is zero, then what is the squ- square of zero? |
| 00:27:07 | Zero. |
| 00:27:08 | Zero. So is there any answer equal to negative? |
| 00:27:11 | No. |
| 00:27:12 | No. So, this answer- this neg- uh, negative four, you cannot find the answers. Okay? |
| 00:27:19 | Because, all the square... |
| 00:27:22 | All the square, you cannot find the negative result. |
| 00:27:26 | Do you have any questions? No. |
| 00:27:29 | So uh, in this case, we just, uh, learned something about the meaning of the square root. |
| 00:27:35 | So that's- what is this meaning of square root? |
| 00:27:37 | So, take square root of nine is to find the number of A such that the square of A is equal to nine. |
| 00:27:45 | So you just take the square root of nine to find the answer. |
| 00:27:50 | And then, uh, if A squared is equal to A, then there are two values. |
| 00:27:55 | So, in this case, it solves the answer is- the answer is positive. |
| 00:27:59 | If this one, there is a negative sign, then the answer is negative. |
| 00:28:04 | Okay? |
| 00:28:06 | Finally, there are some, uh, uh, special, uh, questions for you to think about. |
| 00:28:12 | So you must think carefully that, uh, this answer must be positive because there is no negative sign. |
| 00:28:19 | This one... because inside there is a negative number, then it is- it is, uh- there is no solution. |
| 00:28:29 | Okay, if there is no, uh, questions, |
| 00:28:31 | uh, please go home to read page 163 to page 164. |
| 00:28:56 | Or you can, uh, read these pag- pages now okay? |
| 00:29:00 | So now, please read, uh, page 164 to page 164. |
| 00:29:06 | Uh, in the next lesson, we will learn something about the square root, okay? The properties of the square root. |
| 00:29:50 | At the end. Finished. |
| 00:29:52 | Oh, I- I- I have to wait 'til the end. |
| 00:29:56 | Hmm. Okay. |
| 00:30:35 | Uh, some of you, uh, try to do the class practice, okay? |
| 00:30:44 | So read the pages and do the questions. |
| 00:31:29 | (inaudible) |
| 00:31:52 | Why is it not over yet? [ In Chinese ] |
| 00:33:01 | (inaudible) |
| 00:33:06 | (inaudible) |
| 00:33:07 | (inaudible) |
| 00:33:14 | Okay, this times. |
| 00:33:30 | (inaudible) |
| 00:33:38 | (inaudible) |
| 00:33:45 | Stop joking around! [ In Chinese ] |
| 00:33:53 | Are you for real? [ In Chinese ] |
| 00:34:07 | [ Bell ] |
| 00:34:11 | Ah, it's really bad, don't (inaudible). [ In Chinese ] |
| 00:34:12 | Goodbye class. |
| 00:34:14 | E:00] |