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.

The remainder is 39. It represents that the square of 31 is less than 1000.

The next number is 32 and 32² = 1024

Hence, number to be added to 1000 to make it a perfect square = 32² − 1000 = 1024 − 1000 = 24

Thus, the required number of plants is 24.