The smallest 6 digit number is 100000

We find the square root of 100000 with a calculator:

 = 316.227766

We take the next larger whole number 317

We square 317

317² = 100489

That's the smallest perfect square which is a 6-digit number,
because when we square 316 we only get 99856, which is only 
a 5-digit number.

Answer: 100489

Edwin