Question

A gardener has $1000$ saplings in his garden. Find the minimum number of additional saplings he needs to plant in such a way that the number of rows and the number of columns of saplings remain the same.

• A. $39$
• B. $32$
• C. $31$
• D. $24$

Answer 1

The correct option is D $24$

Since the number of rows and columns of saplings have to be equal, the number of saplings should be a perfect square.
The gardener has $1000$ saplings.
In order to estimate the square root of $1000$, we need to find two consecutive perfect squares between which $1000$ lies.
$961<1000<1024$
We can see that, ${31}^2=961$ and ${32}^2=1024$
$961<1000<1024$
$31<\sqrt{1000}<32$
Hence, required number of additional saplings$=1024-1000=24$
$1000+24=1024$
Hence, the gardener needs $24$ more saplings.