SQUARE AND SQUARE ROOT CLASS 8(EXERCISE6.1 CONT,6.2,6.3) | NCERT | PART 3
SQUARE AND SQUARE ROOT CLASS 8(EXERCISE6.1 CONT,6.2,6.3) | NCERT | PART 3
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00:00Hi everyone, welcome to Insightful Maths.
00:09This is the third session of the chapter Square and Square Roots from Class VIII that we have
00:14already started.
00:15In the previous lectures, I have told you the basics and the introduction of square
00:20and square root, its properties, exercise 6.1 we have already done.
00:26Few of the questions 1 or 2, I have given you as an homework for you to do it yourself.
00:32I'm going to discuss 1 or 2 parts of those questions today as well and then continuing
00:37with 6.2.
00:39If you have not yet liked and subscribed the channel, please like and subscribe.
00:43So I'm starting with exercise 6.2.
00:45Before that, I told you to do these questions.
00:50Question number 5 already discussed.
00:52Question number 6 now I'm discussing here from exercise 6.1.
00:57Have a look at the patterns here.
00:59We need to find this missing number at the second position and the last one.
01:06Now please observe what the pattern is following here.
01:10This last number 2 is converted to 3.
01:132 square is converted to 3 square, likewise 6 square become 7 square, 12 square has become
01:2013 square.
01:21So does it mean 20 square will become 21 square?
01:25Correct.
01:26We have just observed the pattern 2 has become 3, 6 has become 7, 12 has become 30.
01:33So which number will become 21?
01:35It has to be 20 square.
01:37So answer of this number will be 20 square.
01:40Now here you can see 30 has become 31, but we do not know the second part.
01:47There has to be a combination.
01:49Please observe here, 1 multiplied by 2.
01:53It is giving me the third number 2.
01:552 multiplied by 3 is 6.
01:58That means the product of first two numbers is giving you the third number.
02:03We can recheck here, 4 multiplied by 5.
02:06It's 20.
02:07That's our answer.
02:08So 5 multiplied by which number will give you 30?
02:12It has to be 6.
02:14So answer of the second part, this one is 6 square, 5 square plus 6 square plus 30 square
02:21is 31 square.
02:23Now 6 multiplied by 7, 6 into 7 is 42.
02:29So the third number is 42 square.
02:32How we are getting the fourth number?
02:34It is just one digit up, 2 has become 3.
02:38So 42 square will become 43 square.
02:42So answer here to the right-hand side is 43 square.
02:46And once again repeat, first, second, third equal to the fourth number, the product of
02:52first and second number, product is becoming the third number, and third number plus one
02:59is becoming the fourth number.
03:01This is how question number 6 has to be done.
03:04Seventh, I have already discussed.
03:07You just need to count how many odd numbers are repeated.
03:111, 2, 3, 4, 5.
03:13So we have already read this property.
03:16If we are adding the consecutive odd numbers, the how many numbers are repeated, the square
03:22of the numbers will be the sum.
03:24It is 5 number here.
03:25The answer will be 5 square, that is 25.
03:28Accordingly, you can do the third part.
03:31Eighth one, I have already discussed.
03:33Ninth one, I have already discussed.
03:37Coming on to exercise 6.2 now.
03:40You need to find the square of the following numbers.
03:43How do we find the square of a number?
03:46If we have a single digit number, let's say 3, I need to find 3 square.
03:51What is that equal to?
03:523 multiplied by 3, which is 9.
03:55Okay.
03:56Square means the number multiplied by itself.
03:59So if I talk about first part, question number 1, first part, we have to find 32 square.
04:06So one way is 32 multiplied by 32, the traditional method of multiplication.
04:12Let me first get you the answer like this, then I'll use one more method.
04:162 into 2 is 4, 3 into 2 is 6, put across, 3 into 2 is 6 and 3 into 3 is 9.
04:26Now 4 here, 6 and 6 is 12 and 9 plus 1 is 10.
04:32That means the square of 32 is coming as 1024.
04:37If you remember in the previous video, I told you, if any such number is there, you can
04:42split it in two parts.
04:44So one number I'm taking 30, another one is 2.
04:48So it is looking like A plus B whole square.
04:53How do we open it?
04:55First number square plus 2 times multiply first number, second number plus second number
05:03square.
05:04We use this property to find the square.
05:07Now it's not mentioned any property here.
05:10So it's your choice.
05:11Which property do you follow for finding the square?
05:14First number square means 30 square plus 2 times of first number and second number plus
05:24second number square.
05:25Now 30 square means 30 into 30, which is 900 plus 2 into 2 is 4, 4 into 3 is 12.
05:35So product is 120 plus 2 into 2 is 4, 120 plus 4 is 124.
05:42So if I add 900 and 124, 4, 2, 9 plus 1 is 10.
05:49You can have a look, whichever method we adopt, we are getting the same answer.
05:55Question number two, one of the most important question that we generally get in our exams.
06:00It says you have to write a Pythagorean triplet whose one of the member is given.
06:05It's not mentioned that this number is more or less greater whichever.
06:10So you need not to worry.
06:11Just any one combination where the numbers will make the numbers will follow the Pythagoras
06:17theorem.
06:18Which we have already discussed in the previous class.
06:21So if you have not watched that video, you need to watch that first.
06:25Question number two I'm starting with.
06:27Now I gave you the rule in the previous video.
06:30How do we find the Pythagorean triplet?
06:33There is a rule to be followed.
06:37It follows the pattern twice of m, m square plus 1 and m square minus 1 for any value
06:45of m.
06:47This is the rule for the three numbers of a Pythagorean triplet.
06:50We assume now one of the number is given to us as 6.
06:55I can put 6 on any number.
06:57It can be either 2m equal to 6, m square plus 1 equal to 6 or m square minus 1 equal to 6.
07:04Now an easy way out because we need to find the value of m and then putting it here.
07:11But if I put m square plus 1 equal to 6, have a look.
07:15If I write m square plus 1 equal to 6.
07:19So m square will be 6 minus 1 which is 5 and m will be square root of 5.
07:26But I cannot exactly find the square root.
07:28So I should not take 6 equal to this one.
07:32If I take m square minus 1 equal to 6, m square will be 6 plus 1 which is 7.
07:39So m square is 7.
07:41The reverse of square is square root.
07:43So m will be square root of 7 which again I cannot calculate.
07:48So the best option available here is taking 2m equal to 6.
07:52I hope you are able to make out why I am putting 2m equal to 6.
07:56I have just explained putting 6 equal to these two is not getting me the exact value of m.
08:03So you will write let 2m, one of the member of the triplet already given.
08:10This is one of the member.
08:11So one of the member equal to 6.
08:142m means twice of m.
08:16It is multiplied.
08:18So m will be equal to 6 upon 2 which is equal to 3.
08:23After putting 2m equal to 6, we have got the value of 3.
08:27Now for finding the second number which is m square plus 1, third number is m square
08:34minus 1.
08:35Put m equal to 3.
08:38So this is 3 square plus 1 and 3 square minus 1.
08:423 square is not 6.
08:44It is 3 into 3 which is 9.
08:47So 9 plus 1 is 10 and 9 minus 1 is 8.
08:52So we have found the Pythagorean triplet wherein one member was given 6.
08:58Another member we have found 10 and 8.
09:01I will just write it in the ascending order.
09:04That's your answer.
09:06Correct?
09:07Let me do one more part for you so that you find these questions now easy enough.
09:12If I take let's say second part which is 14, again easiest way out because 14 is divisible
09:19by 2.
09:21So second part I am doing.
09:23Let 2m is equal to 14.
09:26So what is the value of m?
09:28It is 14 divided by 2.
09:30That is 7.
09:31First member is already given 14.
09:35m value now is 7.
09:38Second member is m square plus 1.
09:41That means 7 square plus 1.
09:437 square is 7 into 7.
09:46That is 49 minus 1.
09:48So that is equal to 50.
09:51This is your second member of the triplet.
09:55Third member will be calculated m square minus 1.
09:5949 minus 1.
10:01Answer is 48.
10:03So we have got three members.
10:05One member 14 was already given.
10:09Second member is m square plus 1 after putting the value 7 which is 40 and another one is
10:1548.
10:16So you can write the triplet 7, 48 and 60 like this.
10:21That's your answer.
10:23So I hope rest two parts you can do accordingly easily.
10:27Okay.
10:28If not, you can just put in the comment option.
10:31I will redo those questions in the next video.
10:35Coming on to the next slide.
10:37Now there are no more questions in this one 6.2.
10:41It was a small exercise.
10:43Now coming on to the next exercise that is 6.3.
10:476.3 first question you can see here.
10:52What would be the possible ones digit of the square root of each of the following number?
10:59Understand the question.
11:00The question is not asking that a number is given.
11:03You need to find the square in ones digit.
11:05Yeh nahi pucha.
11:07Aapko square is already given.
11:10Question says what will be the ones digit of the square root of the given number?
11:1698.
11:17For example, question number one first part 9801 is given to me.
11:23I need to find the square root.
11:26In fact, without finding the square root, I need to guess jo bhi answer aayega uska
11:32ones digit kya hoga?
11:34Okay.
11:35For doing these questions, please have a look at this statement.
11:40Hume yeh square number given hai.
11:42That means right hand side is given to us.
11:44These all are square number.
11:46Now observe it carefully where I am getting the one at the ones position.
11:53Dekho.
11:54Here we are having one.
11:56Here we are having one.
11:58This is also one.
12:00This is also one.
12:02This is also one and this is also one.
12:04So if I find the root of this number, kaunse number ka square mujhe one deta hai ones position
12:11pe?
12:12When the ones position is either one or nine.
12:16Kyu?
12:17One ka square is one and nine square is 81.
12:22Iski ilawa, I can take the square of any number.
12:25Dekho four square is 16.
12:27Ones digit 6.
12:29Five square is 25.
12:31Ones digit is 5.
12:32But only for two combinations where ones digit should be either one or nine.
12:39My answer will give me ones digit as one.
12:44Theek hai?
12:45So answer here will be question is asking you, question is not asking you the exact
12:51root.
12:52It is asking, what can be the ones digit?
12:55Toh humein square mein one kaha pe milta hai?
12:58When the ones digit of the number should be either one or nine.
13:05One ke square mein ones digit one aati hai.
13:08Nine square also gives me the ones digit one.
13:12Have a look at the second part.
13:14Which number square gives me ones digit as six?
13:18Kis number ke square mein ones digit six aati hai?
13:21Tab aap dekho, ones digit six, kis ke square mein aaya hoon?
13:26Four square.
13:27Ones digit six, kis ke square mein aaya hoon?
13:30Six.
13:31Are we getting ones digit six anywhere else?
13:33Have a look.
13:34Kahe bhi nahi mil raha hoon.
13:35Six mujhe tab milta hai when the ones position is either four or six.
13:40So if the square number is given with the ones digit six aur humein back jaana hai.
13:46So ones digit kya hona chahiye original number ka?
13:50It should be either four or six because four square is what?
13:57Four square is sixteen, ones digit is six and if I take six square, six square is thirty
14:03six, ones digit is six.
14:06I can have as many digits here, hardly makes any difference.
14:10Original number ones digit we are talking about.
14:13Original number ones digit, if it is four and six, the square will end at six.
14:19Then the same question, third part.
14:22Ones digit of the square number is six and if we go back, answer will be same here, one
14:27and nine.
14:28One square bhi one hota hai and nine square is eighty one which will again give you one.
14:33Answer is one and nine here.
14:35Twenty five, this five is very easy.
14:38The square of five will only give you five.
14:41Aap dekho, where do we get square number five?
14:45Jab hum five pe square karte hain, ones digit is five.
14:48No other option.
14:49Fifteen square, ones digit five hai na, square is having ones digit five.
14:54No other option.
14:55So, answer will be only one digit five here.
14:59I hope this much is understood.
15:01Coming on to the second part, without doing any calculation, we have to find which numbers
15:08are not surely perfect square.
15:12You just need to tell, looking at the numbers, paunsi number perfect square ho hi nahi sakte
15:18We have already discussed in the previous videos.
15:21Please have a look.
15:22Perfect square end with zero, one, four, five, six, nine.
15:27Dekho one, four, five, six, nine along with zeros and that too even number of time.
15:34Other than these digits, if we have any other digit at the ones position, the number can
15:39never be a perfect square.
15:41So we are having ones digit three here.
15:44But what do we need?
15:45It should be zero, one, four, five, six, nine, nothing else.
15:52It's not zero, one, four, five, six, nine.
15:54It cannot be.
15:56Once digit seven, not following this criteria, not possible.
16:01Once digit eight, not following this criteria, not possible.
16:05This number is having one, but it doesn't mean it is 100% a perfect square.
16:09It doesn't mean.
16:10It may or may not be.
16:12But these numbers undoubtedly they are not perfect square.
16:16So this number may be a perfect square and we can easily find the square root of this
16:20number.
16:21Here, the answer is not required.
16:24You were just supposed to tell which numbers are not the perfect square.
16:28They cannot be.
16:29So answer is first, second and third.
16:31They cannot be.
16:33Coming to the third question, you need to find the square root of hundred and 169 by
16:39the method of repeated subtraction method is already mentioned here.
16:44So you have to use this method only.
16:47This also we have already done in the previous class.
16:50I'm going to do only one part hundred similarly for 169 you can do.
16:57So hundred, one by one, I keep on subtracting the odd natural numbers, odd consecutive natural
17:04numbers till the time the final number becomes zero.
17:08Next number is one.
17:10So hundred minus one, that is 99.
17:14Start with 99.
17:16The next number is three, 99 minus three.
17:19How to do that?
17:20Nine minus three is six.
17:22Please don't make any error in the calculation, avoid oral calculation, written calculation
17:29may take some time, but that will absolutely be correct one.
17:34So start with 96 now, minus five, one, three, five.
17:40So 96 minus five is how much?
17:43Six minus five is one.
17:45It is 91.
17:47Now 91 minus seven, no error, please.
17:50I know the students doing error at this level.
17:53Okay, so I'm doing it for you like this.
17:56Don't be in a hurry to do the calculation, carry over this become eight and this is 11.
18:01So 11 minus seven, it is equal to four and eight will go down.
18:06So your answer is 84.
18:08Now 84 is the starting number, one, three, five, seven.
18:13Next number is nine, 84 minus nine, again take carry over.
18:18This is seven and 14, 14 minus nine is five, it is 75.
18:25Now beginning number is 75 minus 11, 75 minus 11, five minus one is four, seven minus one
18:34is six.
18:35So you are having 64.
18:38Start with 64 minus 13, 64 minus 13, four minus three is one, six minus one is five.
18:48So you have reached 51 now, 51 minus 15.
18:54Have a look, I'm following the sequence of odd consecutive natural numbers.
18:59Now 51 minus 15, no error, please, I've seen students doing five minus one, four, five
19:05minus one, four, please don't do that.
19:07So this is four now, carry over, it is 11, 11 minus five is six and four minus one is
19:14three.
19:15So we have brought here 36.
19:19Okay, now what you are going to do, start with 36 and subtract 17, because after 15,
19:29the next number will be 17, 36 minus 17, please have a look, this is two, 16 minus seven,
19:37it is equal to nine, two minus one is one, so you have brought here 19.
19:43Start with 19, after 17, the next number is 19, 19 minus 19 is zero.
19:50We have to stop here, once this answer becomes zero, what you are going to do, just count
19:55how many steps we have taken to reach zero, that will be your answer.
19:59It is one, two, three, four, five, six, seven, eight, nine, and 10.
20:06In 10 repeated subtraction, answer has become zero.
20:10So under the root of 100, your answer is 10.
20:14You can do similarly for 169 repeated subtraction, it will go till 13 steps because under the
20:22root of 169 is 13.
20:25Please do it yourself, you can easily do that provided the subtraction here is not having
20:30any error.
20:31Okay?
20:32So please take some time and do the subtraction like this, not orally.
20:36Okay?
20:37Coming on to the question number four now, we have to find the square root of the following
20:42numbers by the prime factorization method.
20:47Square root or using prime factorization also I have already discussed.
20:52So prime factorization, we will do 729.
20:58So many parts are there, so I am going to do only one or two parts because others it
21:03is just a practice game.
21:05You can easily do that yourself.
21:07Okay?
21:08So 729, using the divisibility rule, we can make out this number is divisible by 3.
21:167 plus 2 is 9, 9 plus 9 is 18.
21:20Some of the digits is 18 divisible by 3.
21:23So the complete number can be divisible by 3.
21:26So start dividing by 3, 3 into 2 is 6, carry over 1, 3 into 4 is 12, 3 into 3 is 9.
21:363 into 8 is 24, 3 into 1 is 3.
21:39Please do not use 9 here because we are doing prime factorization.
21:44So you have to use only the prime numbers, 2, 3, 5, 7, 11, 13, likewise.
21:50Okay?
21:51So this is 3 into 2 is 6, 6, 8 minus 6 is 2, 3 into 7 is 21, 3 into 9 is 27, 3 into
22:013 is 9, and 3 into 1 is 3.
22:05So 729, we are finding the square root.
22:08I can write like this, square root of 729.
22:12What all we are getting?
22:132 times 3 here, I'll just write.
22:17This is one pair.
22:19Another pair of 3s, just write like this.
22:22Another pair of 3s, I'm making the pair.
22:26And one more pair of 3, just write 3 into 3.
22:30It has to be written in pair.
22:32Out of these pairs, one number will go out and the square root will get cancelled.
22:38So out of this pair, one 3 out, another pair, another 3 out, another pair, another 3 out,
22:46and the square root got cancelled, another number got cancelled.
22:50So 3 into 3 is 9, and 9 into 3 is 27.
22:56So under the root 729, your answer is 27.
23:01And which method have we used?
23:03That is the prime factorization method.
23:07Please ensure these numbers that you are getting should be the prime numbers only.
23:12For question number 5, it says, for each of the following numbers, you have to find the
23:19smallest whole number by which it should be multiplied so as to get the perfect square
23:25number.
23:26And you also have to find the square root of the number that you are getting.
23:31We have to find which number to be multiplied.
23:37And this number has to become a square number and then we have to find the root of that
23:41number.
23:43So question number 5, first part we are doing.
23:46Most of the parts you will do yourself, it's very easy.
23:50So 252, it's an even number, I can start dividing by 2, 2 into 1 is 2, 2 into 2 is 4, 2 into
24:006 is 12, 2 into 6 is 12, 2 into 3 is 6, 3 into 2 is 6, and 3 into 1 is 3, 3 into 7 is
24:1221.
24:13Please observe it carefully.
24:15So 252 is written as 2 into 2 into 3 into 3 into 7.
24:22Is it a perfect square number?
24:25For every perfect square number, these factors will always come in pair.
24:30Now you see, we are having a pair of 2, we are having a pair of 3, but we are not having
24:36a pair of 7.
24:37So if I multiply this given number by 7, one more 7 will come here and this will also
24:47be paired and this will become a square number.
24:50So question was asking the same thing.
24:52By which number it has to be multiplied to make it a perfect square?
24:57Answer is 7.
24:58So step number 1, you will do the prime factorization.
25:01Whichever number is not paired, you will take the same number.
25:06So answer first part is it has to be multiplied by 7.
25:11Second part of the question is saying you have to find the square root of the number
25:15now.
25:16You have to find the square root as well.
25:22So square root of this number means square root of all this.
25:25And how do we find the square root?
25:28Out of each pair, take one more number out, 2 and 2, 1 out, 3 and 3, 1, 3 out, 7 and 7,
25:357 out.
25:362 into 3 is 6 and 7 into 6 is 42.
25:41That's your answer.
25:42Under root of new number that we have formed after multiplying 7, that is 42.
25:49Rest of the parts are exactly the same.
25:52You can do it.
25:54Question number 6 now says exactly the same question like question number 5.
25:59For each of the following number, you have to find the smallest number by which it should
26:04be divided to get the perfect square.
26:07In the previous question, jo mere paas number paired nahi tha, I have multiplied the number.
26:14Aap next question mein exactly the same step, jo number paired nahi hai na, hum usse sirf
26:20divide kar denge.
26:22Because question is asking by which number you will divide to find the perfect square.
26:28So I am going to do one more part of question number 6.
26:32Rest of the parts, of course, you have to do yourself.
26:35Question number 6, first part.
26:37Given number is 252, even number, I'll divide by 2, 2 into 1 is 2, exactly the same like
26:44we have done here.
26:452 into 2 is 4 and 2 into 6 is 12, 2, 6 is 12, 2, 3 is 6, 3, 2, 1 and 3, 7 is 21.
26:59Number 252 is written as 2, 2, 3, 3 and 7.
27:05Which number is not paired?
27:067.
27:07Agar musse poocha jata by which number I should multiply, so you have to multiply by 7, ye
27:12bhi paired ho jayega.
27:14But question is asking me to divide.
27:15Ab aap dekho yeh number square number kyu nahi hai?
27:19Because one extra 7 is here.
27:21So if I divide this number by 7, so this will also be divided by 7 and this 7 will be removed.
27:29Now the numbers are paired.
27:30So jo number is not paired, aap multiply bhi usi se karte ho and if the question is asking
27:35for division, unpaired number has to be used for division.
27:39So now after dividing by 7, what you are left with?
27:43A pair of 2 and a pair of 3.
27:45So now if I have to find the root of this number, 7 is already cancelled.
27:50So I am left with 2 into 2, 3 into 3.
27:56Out of these 2, 1, 2 out.
27:58Out of these 3, 1, 3 out.
28:00So answer is now 6.
28:04So what you are going to do?
28:06Question number 7, I am leaving for you to understand, to just go through the question
28:11and make out how can this concept will be used for doing this question.
28:16In the next video, I will again be doing few parts of question number 5, 6 and I will discuss
28:22question number 7.
28:24So please watch the next session as well.
28:28And if you have not liked and subscribed, please do this right now.
28:31Thank you so much for following and watching the video.
28:34Take care.