Question

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

Answer 1

Here, plants = 1000

$\begin{array}{cc}& 31\\ 3& \overline{10}\overline{00}\\ & -9\\ 61& 100\\ & -61\\ & 39\end{array}$

Since remainder is 39. Therefore ${31}^2<1000$

Next perfect square number ${32}^2=1024$
Hence, number to be added = 1024 – 1000 = 24

$\therefore 1000+24=1024$

Hence, the gardener required 24 more plants.