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

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 ${\left(31\right)}^2<1000>{\left(32\right)}^2$

It is clear that $1000$ is $\left(124-100\right)24$ less than ${\left(32\right)}^2$

∴ Hence, $24$ more plants are needed.