I would just estimate, and then try out a few in the neighborhood of my estimate until I find it.
My estimate is 320.
3202 = 102,400 too big
3152 = 99,225 too small
3162 = 99,856 too small
3172 = 100,489 just right
The smallest 6-digit perfect square is 100,489.
It's the square of 317.
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1024
100,489 = (317)2
One hundred is the least three-digit square number. It is formed by 102.
121
' 100 ' is the square of 10.