Question

Find the least perfect square with four digits

Answer 1

$\begin{array}{ccc}& 31.6& \\ 3& \overline{10}\overline{00}.\overline{00}& \\ & 9& \\ 61& 100& \\ & 61& \\ 626& 3900& \\ & 3756& \\ & 144& \\ & & \\ & & \end{array}$

The smallest four digit number is 1000,which is not a perfect square as

$\sqrt{1000}=31.6$

Hence the number after $31.6,$ that is ,32's square will be a four-digit perfect square number.

${32}^2=32\times 32=1024$

Hence, $1024$ is the smallest four-digit number which is a perfect square.