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Question

Mathematics Question on Square Roots of Decimals

A gardener has 10001000 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

It is given that the gardener has 10001000 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 10001000 can be calculated by long division method as follows.

| 3131
---|---
33| 1ˉ0ˉ0ˉ0ˉ\bar1\bar0\bar0\bar0
9-9
6161| 100100
6161
| 3939

The remainder is 3939.
It represents that the square of 3131 is less than 10001000.
The next number is 3232 and 32232^2
= 10241024
Hence, number to be added to 10001000 to make it a perfect square
= 32232^2- 1000=10241000=241000 = 1024 - 1000 = 24

Thus, the required number of plants is 2424.