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.

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