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8.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 the same. Find the minimum number of plants he needs more for this.
Answer :

Let the number of rows and columns be x each.
So,the total number of plants =\( x \times x = x^2\)

So we can have, \(x^2 = 1000\)

\(\Rightarrow x = \sqrt{1000}\)

\(\qquad \begin{array}{c|lcr} &31\\ \hline 3 &\;\; \;\bar{10}\bar{00}\\ &\;-9\\ \hline 61 &\;\;\; \;\;100\\ &\;\;\;\;\;61\\ \hline &\;\;\;\;\;39\\ \hline \end{array} \)

We got the remainder as 39. This says that the square of 31 is less than 1000.So, the next number is 32 and \(32^2 = 1024\)

Hence the number to be added = 1024 – 1000 = 24

Thus, the minimum number of plants required by him = 24.