Elliptic Curve Cryptography calculation of $y^2 \equiv x^3 + x + 1 \pmod{23}$

Learning the basics of elliptic curve cryptography. The question is a mathematical one.

While finding the points in the elliptic group $E_{23}(1,1)$,this is how one proceeds :

How is $y^2= 7$ giving $y = 7$? or $y^2 = 8$ giving $y=10$. The perfect squares I can understand but how are the others being calculated? Is it because of $\mod 23$? I am studying the topic from here.