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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.

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.