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1} 2025 plants are to be planted in a garden in such a way that each row contains as many

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plants as the number of rows. Find the number of rows and the number of plants in each

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row.

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2} Find the smallest square number that is divisible by each of the numbers 4, 9 and 10.

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3} Find the greatest 4-digit number which is a perfect square.

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4} Find the length of the side of a square whose area is 441 m

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2 .

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5} A gardener has 1000 plants. He wants to plant these in such a way that the number of

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rows and the number of columns remain same. Find the minimum number of plants he

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needs more for this.

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6} There are 500 children in a school. For a P.T. drill they have to stand in such a manner

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that the number of rows is equal to number of columns. How many children would be left

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out in this arrangement.

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7}  Parikshit makes a cuboid of plasticine of sides 5 cm, 2 cm, 5 cm. How many such

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cuboids will he need to form a cube?

1.The number of plants in each row is equal to the number of rows in the garden.

The total number of plants is 2025. 

Thus, we need to find the square root of 2025

Thus the number of plants in a row is 45 and there are 45 rows in the garden.

2.Let us find the least common multiple of 4,9,10

The factorization of 4 is

The factorization of 9 is 

The factorization of 10 is 

Thus, the least common multiple of 4,9 and 10 is 180.

The factorization of 180 is

We know that 180 is not a perfect square.

There are two 2's and two 3's and one 5 as factors.

To get the square number we can multiply 5 to 180

We got the number 900 which is a perfect square and divisible by 4,9 and 10

3.

We need to find the greatest 4 digit number, which is a perfect square.

Greatest 4 digit number is 9999.

But 9999 is not a perfect square.

Find the approximate value of the square root of 9999.

Thus, the approximate value of the square root of 9999 is 99.999...

Now let us find the square of the number 99.

Thus the square of the number 99 is 9801.

Therefore, 9801 is the greatest 4 digit square number.

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1. 45

2. ?

3. 99

4. 21

5. 31 but minimum is 4

6. 16

7. i think 2

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1.45

2.not possible

3. 9801

4.21

5.31>4

6.16

7.20cuboids

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 1. 45

 2. find the L.C.M of 4, 9 and 10.

L.C.M is 180

180 is not a square number

to make it a square number multiply it with 5

the answer is 900

900 is divisible with 4 , 9 and 10.

 3. 9801

 4. 21

 5. first using the division method try to find the square root of 1000.

You will get the square root as 31 and remainder as 9.

Find the square of the next number after 31 which is 32

The square is 1024

Subtract 1000 from 1024

You get the answer as 24

The gardener needs a minimum of 24 plants.

 6. 16 children will be left out.

 7. we need 10 cuboids so as to make the sides equal.

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ok, the 3rd answer for mine is wrong...careless mistake...and also the 7th one....i dont know that one

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  •  45
  • find the L.C.M of 4, 9 and 10.
  • L.C.M is 180
  • 180 is not a square number
  • to make it a square number multiply it with 5
  • the answer is 900
  • 900 is divisible with 4 , 9 and 10.
  •  9801
  •  21
  •  first using the division method try to find the square root of 1000.
  • You will get the square root as 31 and remainder as 9.
  • Find the square of the next number after 31 which is 32
  • The square is 1024
  • Subtract 1000 from 1024
  • You get the answer as 24
  • The gardener needs a minimum of 24 plants.
  •  16 children 
  •  we need 10 cuboids so as to make the sides equal.
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  1. 45
  2. 900
  3. 9801
  4. 21
  5. 24
  6. 16
  7. 10
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 . 45

2. find the L.C.M of 4, 9 and 10.

L.C.M is 180

180 is not a square number

to make it a square number multiply it with 5

the answer is 900

900 is divisible with 4 , 9 and 10.

3. 9801

4. 21

5. first using the division method try to find the square root of 1000.

You will get the square root as 31 and remainder as 9.

Find the square of the next number after 31 which is 32

The square is 1024

Subtract 1000 from 1024

You get the answer as 24

The gardener needs a minimum of 24 plants.

6. 16 children will be left out.

7. we need 10 cuboids so as to make the sides equal.

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