(*Using the fixed point iteration to find the square root of 2*)

Remove["Global`*"]
a=2;
f[x_]=x^2-a;
g[x_]={0.5(x+(a/x)),0.5(x+(a/x))};
list={{"k","g1", "g2"}};
kmax=3;
xold={-1,1};
For[k=1,k≤kmax,++k,
For[i=1,i≤2,i++,
xnew[i]=g[xold[[i]]][[i]];
xold[[i]]=xnew[i];
];
AppendTo[list,Flatten[{k,Table[g[xnew[j]][[j]],{j,1,2}]}]]
]
Grid[list,Frame->All]