I found this problem asking to complete the square root of a square number. I have found some numbers but at this point I'm stuck.
I could brute force my way through, looking for numbers between $3163$ (the smallest with an $8$-digit square), and $3199$ which end in $36$ when squared, but I would like to know if there is enough information to complete the diagram.
Any help would be appreciated!
The ones digit of the square root has to be $4$ or $6$ to make the ones digit of the square be $6$. Then we know that a number that ends in $06$ will have a square that ends in $36$ so a number that ends in $94$ will, too. None of $16^2, 26^2, 36^2, 04^2, 14^2, 24^2, 34^2$ end in $36$ so no other bottom two digits will work. I used the fact that I know the small squares and negating a square root leaves the square unchanged.