Question

8. A gardener has 1000 plants. He wants to plant these in such a way that the numb
of rows and the number of columns remain same. Find the minimum numbers
plants he needs more for this.​

Answer 1

Total plants = Number of plants in 1st row

+ Number of plants in 2nd row

+ Number of plants in 3rd row

= 3+3+3

=3×3

=9

So we can say that

Total plants = Number of rows × Number of column

Given

Total plants = 1000

And number of rows is equal to the number of columns

let number of rows = x

number of column = x

Now,

Total plants = Number of rows × Number of

column

1000 = x × x

1000 =

${x}^{2}$

${x}^{2}$

= 1000

Finding square root of 1000 using long division

1000 ÷ 3 = quotient = 31 and remainder = 39

we need to find

the least number that must be added to 1000 so as to get a perfect square

Now,

${31}^{2}$

$<$

$1000$

$<$

${32}^{2}$

Thus, we add

${32}^{2}$

$-$

$1000$

$= 1024 - 1000$

$= 24$

Therefore, the gardner need 24 more plants

Answer 2

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

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1000 is not a perfect square.

$\implies \tt{ {31}^{2} < 1000 < {32}^{2} }$

Number to be added:-

$\implies \tt{1024 - 1000} = 24$

$\implies \tt{ 1000 + 24} =10 24$

Hence, Gardener requires 24 more plants.

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