Question

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.

Answer 1

It is given that the gardener has \(1000\) plants. The number of rows and the number of columns is the same.
We have to find the number of more plants that should be there, so that when the gardener plants them, the number of rows and columns are same.
That is, the number which should be added to 1000 to make it a perfect square has to be calculated.
The square root of \(1000 \) can be calculated by long division method as follows.

	\(31\)
\(3\)	\(\bar1\bar0\bar0\bar0\) \(-9\)
\(61\)	\(100\) \(61\)
	\(39\)

The remainder is \(39\). 
It represents that the square of \(31\) is less than \(1000\).
The next number is \(32\) and \(32^2\)
= \(1024\)
Hence, number to be added to \(1000\) to make it a perfect square
= \(32^2\)- \(1000 = 1024 - 1000 = 24\)

Thus, the required number of plants is \(24\).