Extracting an expression matching a pattern from a large expression

Question

I have a Mathematica expression that contains a single square root, schematically

expr = a / (b + Sqrt[c]);

where a,b

Answer 1

I await a few examples, but in the meantime, try:

Cases[expr, x_^(1/2 | -1/2) :> x, Infinity]

The standard internal form for Sqrt(x) is Power[x, 1/2].