(1)If your vectors x and x follows exactly z=c*sqrt(x), then the constant c can be calculated, as mentioned by Adam Danz,
You have a vector c which has 10 identical value which is what you are looking for.
(2) In the case x, and z just follow then trend of z=c*sqrt(x), you are actually asking for a constant c that minimize some function of the error
vector. Normally, we minimize norm of the square of the error 
. This is a least square problem. You can actually use the curve fitting tool box to fit the function. sqrtX = sqrt(x);
f = fit(sqrtX,z,'poly1');
c = f.p1;
Here is my little example.
x = (1:10)';sqrtX = sqrt(x);
z = 2*sqrtX+0.05*randn(10,1);
f = fit(sqrtX,z,'poly1');
c = f.p1
ans =
1.9725
The parameter c = 2 was calculated to be 1.9725.
