We construct a 2-qubit entangling gate by approximation with Fibonacci anyons. To do so, we need an approximation of two gates, namely the Hadamard gate and the Pauli X gate. From an approximate Pauli X gate, we can derive an approximation of the Bell state, which is extensively used in the protocol which we develop. As a sort of converse, we show that if we had an exact Bell state, then we would be able to produce the Pauli X gate accurately. Along the way, we also show how to turn ancillas with adequate norms ratio into phase gates, assuming the Bell state is available exactly.