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Squares and Square Roots | Exercise 6.4

Question 16

Q8) A gardener has 1000 plants. He wants to plant these in such a way that the number of rows and the number of columns remains the same. Find the minimum number of plants he needs more for this.

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  • Solution

  • Transcript

Solution:

Here, plants = 1000

Since the remainder is 39.

Therefore 31^2<1000

Next perfect square number 32^2=1024

Hence, number to be added

= 1024 – 1000 = 24

\therefore1000+24=1024

Hence, the gardener required 24 more plants.

Hello kids, welcome to Lido homework in this video we are going to answer this question that states a the gardener has a thousand plants he wants to plant these in such a way. that he has An equal number of rows and an equal number of columns okay find the minimum number of plants he needs more for this so instead of trying to imagine a thousand plants, let's imagine if you have four plants can you arrange them in an equal number of rows and equal number of columns if you have four plants can you do something like this great okay what if I tell you that I'll give you five plants can you arrange them in an equal number of rows and an equal number of columns no right if there are five then you will have to add in some more plans to make An equal number of rows and an equal number of columns right but if it was only 4 then you can See you over here 2 rows and 2 columns also pay attention 4 is a perfect square so you can conclude that for an equal number of rows and an equal number of columns the number of plants whatever the number of plants it should be a perfect square when I told you I'd give you one more plant That's nothing but five plants and five is not a perfect square right so you will have to add in more plants to figure out how you will make the perfect same number of rows and the same number of columns okay so in this case what would you do obviously you have five you will add in four more right and then you will make it into three rows and three the column that is again nine so the idea here is to have an equal number of rows and The equal number of columns the number of plants should be perfect square so let's first check if a thousand is a perfect square if you read the question carefully the question itself says to find the minimum number of plants he needs more for this right that means Definitely a thousand is not perfect square but we need to figure out uh how many more plants will he need right so let's get into that and for what will you do, you will take the number thousands and then we'll first find out using the long division method what could be the possible number of plants he needs to add so let's take thousands here and we'll do the long division method so for long division method first pair up all the numbers in groups of twos from your right to left so one pair and another paris the second step is to find the perfect square closer to 10 so these three are nine I'll get one and I'll bring down the next pair that's a hundred the next step is to multiply your quotient with two you will get it as six now we need to figure out another number over here when you will multiply it you will get a number that is less Then 100 so that is 61 into 1 The rights will give us 60 1 and the The rest here is 39 so now since there is a remainder that means that this is not perfect. square we need to find out how many more um plants that he will need now since this is 39 as a rest we can see that 31 square will for sure be less than the number given to us that's a thousand Okay, let's move on to the next number after 31 and that's 32 square 32 square is 1024 okay so I can say that 1000 actually lies between 31 square and 32 square so the number of plants additional that the gardener needs should be a Perfect Square like we said and the next The immediate perfect square after 31 is 32 which is 1024 and it's more than a thousand right so how many more plants will he need let's take 1024 minus thousand which is equal to 24 right so a thousand plants that he has he will add in 24 more plants right He will have 1024 plants and now with this 1024 plants, how many rows and how many columns he can make since the perfect square right its 32 square is 1024 so that means that he can make a number of rows and number of columns equal if he add 24 more plants to 1000 okay hope your doubt for this particular question uh is resolved please feel free to like share and comment and I'll see you in another video

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Question 16

Q8) A gardener has 1000 plants. He wants to plant these in such a way that the number of rows and the number of columns remains the same. Find the minimum number of plants he needs more for this.

  • Solution

  • Transcript

Solution:

Here, plants = 1000

Since the remainder is 39.

Therefore 31^2<1000

Next perfect square number 32^2=1024

Hence, number to be added

= 1024 – 1000 = 24

\therefore1000+24=1024

Hence, the gardener required 24 more plants.

Hello kids, welcome to Lido homework in this video we are going to answer this question that states a the gardener has a thousand plants he wants to plant these in such a way. that he has An equal number of rows and an equal number of columns okay find the minimum number of plants he needs more for this so instead of trying to imagine a thousand plants, let's imagine if you have four plants can you arrange them in an equal number of rows and equal number of columns if you have four plants can you do something like this great okay what if I tell you that I'll give you five plants can you arrange them in an equal number of rows and an equal number of columns no right if there are five then you will have to add in some more plans to make An equal number of rows and an equal number of columns right but if it was only 4 then you can See you over here 2 rows and 2 columns also pay attention 4 is a perfect square so you can conclude that for an equal number of rows and an equal number of columns the number of plants whatever the number of plants it should be a perfect square when I told you I'd give you one more plant That's nothing but five plants and five is not a perfect square right so you will have to add in more plants to figure out how you will make the perfect same number of rows and the same number of columns okay so in this case what would you do obviously you have five you will add in four more right and then you will make it into three rows and three the column that is again nine so the idea here is to have an equal number of rows and The equal number of columns the number of plants should be perfect square so let's first check if a thousand is a perfect square if you read the question carefully the question itself says to find the minimum number of plants he needs more for this right that means Definitely a thousand is not perfect square but we need to figure out uh how many more plants will he need right so let's get into that and for what will you do, you will take the number thousands and then we'll first find out using the long division method what could be the possible number of plants he needs to add so let's take thousands here and we'll do the long division method so for long division method first pair up all the numbers in groups of twos from your right to left so one pair and another paris the second step is to find the perfect square closer to 10 so these three are nine I'll get one and I'll bring down the next pair that's a hundred the next step is to multiply your quotient with two you will get it as six now we need to figure out another number over here when you will multiply it you will get a number that is less Then 100 so that is 61 into 1 The rights will give us 60 1 and the The rest here is 39 so now since there is a remainder that means that this is not perfect. square we need to find out how many more um plants that he will need now since this is 39 as a rest we can see that 31 square will for sure be less than the number given to us that's a thousand Okay, let's move on to the next number after 31 and that's 32 square 32 square is 1024 okay so I can say that 1000 actually lies between 31 square and 32 square so the number of plants additional that the gardener needs should be a Perfect Square like we said and the next The immediate perfect square after 31 is 32 which is 1024 and it's more than a thousand right so how many more plants will he need let's take 1024 minus thousand which is equal to 24 right so a thousand plants that he has he will add in 24 more plants right He will have 1024 plants and now with this 1024 plants, how many rows and how many columns he can make since the perfect square right its 32 square is 1024 so that means that he can make a number of rows and number of columns equal if he add 24 more plants to 1000 okay hope your doubt for this particular question uh is resolved please feel free to like share and comment and I'll see you in another video

Our top 5% students will be awarded a special scholarship to Lido.

subject-cta
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