In this talk, I introduce triple quadratic residue symbols for certain primes in a real quadratic field $k$ with narrow class number one. Our symbol may be regarded as a triple generalization of the quadratic residue symbol in $k$ and also an extension of the R\'{e}dei symbol in the rationals for $k$. From the viewpoint of arithmetic topology, our symbol may be regarded as an arithmetic analogue of Milnor--Turaev's triple linking number of knots in a homology 3-sphere. For the construction, we determine the group presentation of the pro-2 maximal Galois group over $k$ with restricted ramification, from which we derive our triple symbols by using mod 2 Magnus expansion. We then show that our triple symbol describes the decomposition law of a prime