SQUARE AND SQUARE ROOT CLASS 8(EXERCISE 6.3 CONT,6.4) | NCERT | PART 4
SQUARE AND SQUARE ROOT CLASS 8(EXERCISE 6.3 CONT,6.4) | NCERT | PART 4
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00:00Hi everyone. Welcome to Insightful Maths. In the previous sessions, we have already
00:06finished square and square root few of the exercises like 6.1, 2. These are completed.
00:13For 6.3, we have already completed till question number 6. Now, I am going to start from question
00:19number 7. So, I hope you have understood the topics till now, question number 5 and 6.
00:25If not, I request go through the video once again and practice the questions. Just to
00:29quick recap, in question number 5, what was to be done? For example, I have a number 8.
00:36Okay, I have a number 8. After prime factorization, I am getting it something like 2 x 2 x 3.
00:43Just for an example, I am taking. Question is saying, this number has to be multiplied
00:49by which number so that it becomes a perfect square. A perfect square number always have
00:55its prime factors in pairs. Now, we can see that 2 is paired but 3 is not paired. So,
01:01if I multiply this number 8 by 3, 1, 3 will be multiplied with the prime factorization
01:08and it will become a perfect square. So, whichever number is not paired, you have to multiply
01:13by that number. In the similar manner, question number 6, again you will be doing the prime
01:19factorization of the given number like same example, I am taking 2 x 2 x 3. Question says,
01:26it has to be divided by which number so that it becomes a perfect square. Which number is not
01:33paired here? 3. So, if I divide this by 3, so that means this is also divided by 3. 3 and 3 will be
01:41cancelled and the rest of the numbers will be paired and it will become a perfect square. Only
01:46this rule we will be using in both the questions. Coming to question number 7, it says, in a class,
01:53students donated in total 2401 rupees. This is the total collection. For the Prime Minister's
02:01National Relief Fund, each student donated as many rupees as the number of students in the
02:07class. Question says, find the number of students in the class. What is the meaning of the question?
02:13Please understand, if the number of students and the money they have donated, the value has to be
02:21equal. For example, if 10 students are there in the class, each student will be donating 10 rupees.
02:28So, what is the total money? 10 students and each has given 10. So, final amount has to be 100. How
02:36we are getting final amount? Number of students multiplied by the money per student has contributed.
02:43For example, 20 students are there in the class. So, each student has to pay 20 rupees. So, that
02:50means 20 will be repeated 20 times. Total collection will be 400. But now, the number of students are
02:56not known. Let's take the number of students as X. As per the question, whatever is the number of
03:05students, if this is the number of students, then the amount of collection also has to be equal.
03:12That means, if X students are there, each student has contributed X rupees only. Okay. So, total
03:20collection has to be equal to X multiplied by X and the value is given as rupees 2401. We know
03:30X multiplied by X. Two similar numbers when they get multiplied, it becomes a squared number. So,
03:37this will be equal to X square which is equal to 2401. But we do not need the value of X square.
03:45We need the value of X. So, this square we need to remove. What is the opposite of square? That
03:53is square root. Have a look here. 2 square is equal to 4. And what is under root of 4? That is
04:012. Okay. So, if a square is removed, if I am removing the square from here, it is going at
04:08under root on another side. So, X will be equal to under the root 2401. Okay. Now, let me prime
04:18factorize 2401 for you. For that, you should have the command on the multiplication tables. Okay.
04:25Otherwise, you will get confused. 2401 is divisible by which number? It comes through
04:30practice only. 2401, this number is a multiple of 7. So, it has to be divisible by 7. 7 into 3 is
04:4121. Carry over 3, it becomes 30. 7 into 4 is 28. 2 left out. So, this is 21. 7 into 3 is 21.
04:51Divide this number by 7 once again. 7 into 4 is 28. 63 is left out. 7 into 9 is 63. 49 divided by
05:027 and 7 divided by 7 is 1. So, under the root 2401 is 7, 7, 7 and 7. How do we get square root?
05:14Make a pair of 22 numbers. Out of 22 numbers, 11 will come out. So, that is 7 from this pair
05:22and 7 from another one. Answer is 49. The value of X, the number of students is equal to 49. So,
05:32whenever the money contributed number of students, two things are getting multiplied and both having
05:38the same value. It becomes a squared number. And what is the opposite of square? That is square
05:43root. I hope this is understood. Let's go to the next question. Question number 8 is exactly
05:51similar. It says 2025 plants are to be planted in a garden. In such a manner, number of rows and
05:59number of columns should be equal. So, you need to find how many rows and the how many plants in
06:05each. Understand, let's say I have 3 rows. 1, 2 and 3. Question says, such a way each row contains
06:16as many plants as the number of rows. If 3 rows I have made, then 3 plants should be there in each
06:23row. Please understand through this example. So, in total how many plants are there? 3 rows multiplied
06:30by 3 plants in each row. So, 3 into 3 is equal to 9. In the similar manner, let's say 4 rows. I am
06:39making it 4 now. So, if 4 rows are there, each row has to have 4 plants. So, how many total plants
06:47are there? Number of rows multiplied by number of plants in each row. So, total plants are 60.
06:54Okay, how we are getting total plants? Number of rows multiplied by number of plants in each row.
07:04That is the total number of plants and which is given to you as 2025. In this particular case,
07:14these things are equal. It is given to us and we need to find how many rows and how many plants
07:20are there. If I take rows as X, we can see here the number of rows and the number of plants are
07:27same. X rows multiplied by X plants, it is given 2025. That means X square is 2025. Opposite of
07:39X square is square root. So, X is equal to under the root 2025. If I find 5 under the root, these
07:48numbers are multiple of 5. 5 into 4 is 20. One very important thing. This will not be written
07:57as 45. The general error students do. Have a look here. If you divide 2025 by 5, 5 into 4 is 20.
08:07Difference is 0 and 2 on down. After taking the difference and borrowing the digit down,
08:13this number has to be divisible by 5. But I cannot. In this particular scenario, I need to borrow one
08:22more digit down and I put a 0 here. After taking a 0, I can borrow another digit. Now 5 into 5 is
08:3025. This is how it has to happen. So, number here is 405. It's not 45. 5 into 8 is 40 and it is 1.
08:413 into 2 is 6. 3, 6, 7, 8, 23. 7 is 21. 3 into 9 and then 3 into 3. So, under root of 2025 can be
08:57written as 5, 5, 3, 3, 3 and 3. Make the groups. 1 group, 2 group, 3 group. Out of each group,
09:08each number will come out. 1, 1 digit. 5, 3 and 3. 5 into 3 is 15. 15 into 3 is 45. That's your
09:18answer. Okay? So, there are 45 rows and each row is having 45 flats. Exactly similar like the
09:27previous question. Question number 9, I give you as homework. Why? Because I am doing question
09:33number 10 which is exactly similar to question number 9. Okay. Now, before doing question number
09:4110, let us understand a very important topic. If I am being given 2 numbers. If I am having 2
09:50numbers, let's say 2 and 3 and I have to find the smallest number which is divisible by both.
09:57Sabse chota number jo in dono se divide ho jayega. Aap dekho, table of 2 goes like this. Table of 3
10:07goes like this. So, which is the smallest number common in both? It is 6. Dono ki table mein hai and
10:15it is divisible by both. So, in whichever question you are asked to find the number which is divisible
10:22by all the given numbers, you need to find the least common multiple. I have already made the
10:29video on this topic. If you have not seen that, please go there and see that video. You should
10:35know how to find the LCM of given numbers. Numbers given here are 8, 15 and 20 but one
10:42clause is there. You have to find the smallest square number. Smallest number is LCM but LCM
10:51may or may not be a square number. Square number kya hota hai? Which is a perfect square. Jiske
10:57multiples will be paired. Thehne LCM nikalte hain then we will go ahead. Numbers given are 8,
11:0415 and 20. Let's start dividing. 2 x 4 is 8. 15 as it is, it is 10. 2 x 2 is 4. 16 as it is,
11:17it is 5. Now, 2 x 1. 15 and 5 as it is. Now, divide by 5. 1, 1 and 3. Now, finally divided
11:29by 3. You can change the order. Hardly matters. The answer will be same. LCM is the product of
11:36all these numbers. 2, 2, 2 and 5 along with 3. Please recheck. We should not miss on any
11:44of the numbers. 1, 2, 3, 4, 5. You are having 5 numbers here. Another important clue. A
11:51combination of 2 and 5 is there. Multiply these two first for making your calculation easier.
11:572 x 2 is 4. 4 x 3 is 12 and 12 x 10 answer is 120. Thik hai? Till now I hope it is understood.
12:09If you are finding the least number which is divisible by all, you need to find the LCM.
12:16Now, what we are going to do? This LCM should be a squared number. Question says this LCM has to
12:24be a squared number. I need not to do any prime factorization. It is already there with me.
12:31Now, we look for the numbers which are not paired. Please have a look. This 2 is paired. Other than
12:39this, pair of 2 is missing, pair of 5 is missing, pair of 3 is missing. I need to make it a squared
12:47number. So, what we are going to do? Like we have done in question 5. If I multiply this number by
12:551, 2, this will be paired. 1, 5 paired and 1, 3 paired. So, if I multiply the given number by
13:03all these three, this will become a squared number. The prime factorization of squared number,
13:11the prime factors should be grouped. Here, these numbers are not grouped.
13:16To jo bhi number group nahi hai, we have to take that number. 5 x 2 is 10 and 10 x 3 is 30.
13:25So, this number, if I multiply 120 by 30, it will become a squared number. 12 x 3, it's 36.
13:3510 here and 10 here, two zeros and it is a squared number. Okay. So, question was finding the
13:43smallest squared number which is divisible by all these. Step number 1, find the LCM. Now,
13:50check in your LCM which numbers are not paired. Juska bhi pair missing hai, you have to multiply
13:58by those numbers and this is your final answer. Your final answer is not 30. Please understand.
14:04We are finding the smallest squared number. Yeh wala number hai, final answer which is divisible
14:10by all three. Okay. Similarly, you have to do question number 9 exactly on the same ground.
14:17Find the LCM and after that, make the pairs. Okay. Question number 1 of exercise 6.4, we are
14:27starting now, where we have to find the square root by division width. Okay. Question number 1,
14:35first part. 2, 3, 0, 4. I have already explained this in the previous videos, how to find the
14:45square root by this method, division method. What you are going to do, you have to make a group of
14:532, 2 numbers starting from right-hand side. First group, second group. Please understand,
14:59group has to be made from right-hand side. First group and second group. Look for a number,
15:06the square of that number should either be equal to 23 or lesser than 23. It should not exceed.
15:13So, 3 x 3 is 9, 4 x 4 is 16, 5 x 5 is 25. But 25 is more. So, we have to start from 4.
15:224 x 4, that is 16. Take the difference, 23 – 16. It is 7. Now, the second group,
15:33not a single digit, the complete group will go down. Now, my new number is 704.
15:41Which number I have to start with? Double of the given number. What is double of 4? 2 x 4. It is
15:478, a dash here. Now, whatever digit we put here, this complete number has to be multiplied by that
15:57digit. What does it mean? If I put 1, so 81 x 1. If I put 2, 82 x 2. Now, have a look, the product
16:08should end in 4. The square of which number gives me one digit 4? If I do 8 x 8, I get 64,
16:24one digit 4. I need one digit 4. So, I can just guess or estimate. Let me try putting an 8 here.
16:3388 x 8. Let us just give it a try. 8 x 8 is 64. One digit is matching. 6 up. 8 x 8 is 64
16:44plus 6. Wow! We have got the same number 704. So, estimation really helps. Put 8 here. Whichever
16:52digit you are putting here, that will go up. So, 88 x 8 is 704 and it is solved. So, what is your
17:01answer? Square root of 2304 is 48. Let us do one more part of this question. So many parts are
17:11there and of course, you need to practice all the parts on your own. Let us do this one. It is 3,
17:204, 8, 1. Third part we are doing. Make a group of total digit starting from the right hand side,
17:28two digit here, two digit here. After that, we have to make a division table like this.
17:36Alright! Now, looking for a number, square of a number which is equal to 36.
17:446 x 6 is 36. 5 x 5 is 25. I cannot go till 36. So, 5 x 5 is 25. Take the difference.
17:5614 minus 5. It is 9. Difference is 9. Now, this complete set will go down. My number is 981.
18:07Now, which number I have to start with? Twice of the given number. What is double of 5? It is 10.
18:15After 10, you have to put a blank here. 10 x which number? The number you put here,
18:22that has to come here only. 1's digit is 1 here. How do we get 1 at 1's place?
18:291 square is 1 and 9 square is 81. 81 means 1's digit is 1. Okay! So, we get 1 at the 1's place
18:40if we are getting the square of 1 or 9. 101 x 1 is 101. It is not matching here.
18:47I try with 9 here. 9 x 9 is 81. 9 x 0 is 0. 8 as it is and 9 x 1 is 9. Have a look. It is matching.
18:58So, please use the estimation method for guessing that this is the square of which number.
19:04You have to put a 9 down, a 9 up and your answer is 981 and it is done. So, what's your answer?
19:14Your answer is 59. I hope this method is understood. Please do rest of the parts.
19:21Let me move to the next question. Okay! Now, in question number 2, it's very easy.
19:30You have to find without actually finding the square root of the given number
19:35that in the square root of this given number, how many digits will be there? An easier way out is
19:43for let's say the number is 64. If the number of digits are even, so formula is n upon 2.
19:55If the number of digits are all, so what you are supposed to do? The number of digits plus 1.
20:02Make it an even number and then divide it by 2. What does it mean? How many digits are there? 2.
20:09So, 2 divided by 2. Answer is 1. The square root of this number will be a one-digit number.
20:16How many digits? 3. 3 is an odd number. Let's make it even. 3 plus 1 by 2. It is 4 by 2
20:25and 4 by 2 is what? It is just 2. So, this will have 2 digits in its square root. Okay!
20:33Another way out is 2, 7, 2, 2, 5. If you remember, when we find the square root,
20:42we start pairing up the numbers starting from right-hand side. Let us make the pair. First pair,
20:49second pair and this is left alone a single pair. How many pairs were able to find? 3 pairs. That's
20:55your answer. If I go by the rule, 1, 2, 3, 4, 5 digits are there. 5 is an odd number. So, 5 plus
21:071 upon 2. That is 6 by 2 and 6 by 2. Answer is 3. Again, the same answer. Okay! So, if the number
21:16of digits are even, half the number of digits, number of digits are odd, number of digits plus
21:221 by 2. Okay! Now, finding the square root of the decimal numbers. Exactly the same process
21:33but the pairing up, there is a difference in pairing up. Have a look. I am starting with
21:392.56. Question no. 3, first one. How the pairing has to be done? This left-hand side of the decimal
21:48will be paired the way we have done. Okay! If it is let's say a 3-digit number like this. So,
21:54we will make the first pair and second pair. Okay! And let's say it is a 3-digit number like this.
22:01On the right of decimal, we start making the pair from here. Why is that so? Because I can put as
22:09zeros here myself and it can be paired. Okay! Once again, let's say the number is 163.261.
22:17I am just picking a random number for you to understand how the pairing has to be done.
22:23Left-hand side, two numbers, one number. Right-hand side, pair from here. One pair,
22:30make a zero, second pair. Understood how the pairing has to be done? Now, let's do this given
22:37question which is 2.56. One of the way you can do is, we have to find under the root 2.56. It
22:47can be done under the root 256 upon. After the decimal two digits are there, you can write 100.
22:56So, under the root 256 divided by under the root 100. What is under the root 100? 100
23:05square. 10 into 10 is 100. So, whatever comes under root of 256, you need to divide by 10.
23:12Okay! One method is this one. Another one, I am doing from the division method directly.
23:18Please have a look. It is 2.56. One digit only, one pair, second pair. Pairs are done. Now,
23:28you have to make the division symbol. Alright! Which square number will give me 2? 2 square is
23:364. So, I have to start with one square only. 1 into 1 is 1. Difference is 1. Now, I have to
23:44take this pair down. But there is a decimal which is bothering. So, decimal will be shifted to the
23:50answer. Now, you can take 56 down. Exactly the same process. Double of 1 is 2. We have to start
23:59from 2. A digit has to be inserted here. How do we get 6 at the 1's position? 4 square is 16.
24:10It gives 1's position as 6. 6 square is 36. Again, we get 6. No other option is possible.
24:19So, either you can try with 4 or you can try with 6. If I try by 4, 4 into 4 is 16. 4 into 2 is 8
24:29plus 1 is 9. Quite smaller. Not matching. Try with 26. 6 into 6 is 36. 6 into 2 is 12 and 3 is 15.
24:41Are we getting the answer? So, we have put 6 down, 6 up and it has given me 156 and it is solved.
24:50Your answer is 1.6. Okay! So, in this manner, we can solve these questions. I think for today,
24:58this much is okay. Once you practice the given questions, only then it is fruitful, only then
25:04it is useful to go ahead. Because the next questions are something like, if you do not
25:10have command on these topics till here, you won't be able to understand these questions.
25:15So, I request whatever we have done so far, complete that up. In another video, we will be
25:21able to finish up this chapter with all the questions. Okay! So, please practice till here.
25:28The square root of the decimal numbers. In the next video, I will do one more decimal expansion,
25:34the square root of the decimal number and rest of the questions. Alright! If you have not liked
25:41and subscribed yet, please do like and subscribe and see the next video. Thank you so much for
25:47watching. Take care!