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.

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Solution

Let's find the minimum number of extra plants he needs :
Let the number of rows and columns be $x$ .
Total number of plants $= x^{2}$
$x^{2} = 1000$
$x = \sqrt{1000}$
We note that ${(31)}^{2} < 1000 > {(32)}^{2}$
It is clear that $1000$ is $(124 - 100) 24$ less than ${(32)}^{2}$
∴ Hence, $24$ more plants are needed.

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