Question

7- 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. Same find the minimum number of plants he needs more for
this​

Answer 1

■ Given ■

A gardener has 1000 plants.He wants to plant them that the number of rows and the number of colums remain.

■ To find ■

Should find the minimum number of plants he need for this.

$\huge\bf{Answer}$

Sum starts -

Given in the sum -

Total plants - 1000 plants.

Number of rows and columns are equal.

Number of rows be - x

Number of Columns be - x

To know the number of plants we should multiply the number of rows and the columns

So - Number of rows × Number of plants.

$1000 = x \times x \\ 1000 = {x}^{2} \\ {x}^{2} = 1000 \\ x = \sqrt{1000}$

Let us now find Square root of 1000 by a long division method.

We got the remainder = 39

Now see we got in this question as how much he needs more?

So obviously we need to find the small or the least number which had to be added for 1000 to get one square.

31^2 < 1000 < 32^2

We should add 32^2 - 1000

= 32^2 -- 1000

= 1024 - 1000

= 24

Therefore ,He needs other more 24 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.