Ross County booked their place in the last 16 of the Scottish Cup with a glut of goals against fourth round opponents Dundee United at Global Energy Stadium.A hectic first half produced six goals, four of them to County, and despite a gallant second round performance from the Championship side, County finished strongly to seal their place in the next round.County took the lead in spectacular style in the sixth minute when a Martin Woods corner fell for the unmarked Christopher Routis who fired an unstoppable shot high into the net from just inside the 18-yard box.Liam Boyce burst into the United box shortly afterwards but he blasted his shot well over the crossbar. United were seldom seen as an attacking force but Stewart Murdoch let fly from distance just before the break but his effort flew wide of Fox’s right hand post.But United reduced the deficit in first half stoppage time when Routis gave the ball away at the back and Andreu took full advantage and raced clear to score for his second of the afternoon.Both sides made changes at the start of the second half with new signing Jim O’Brien and Reghan Tumilty on for McEveley and Woods, while Willo Flood and Thomas Mikkelsen replaced Murdoch and Obadeyi.Buoyed by the goal just before the break, United piled the pressure on and William Edjenguele headed over a Fraser cross immediately after the restart.The Tangerines looked the most likely to score and they came close in the 63rd minute when a Flood shot was deflected into the path of fellow sub Mikkelsen but the big forward failed to control it and the ball ran harmlessly out.At the other end, Schalk found space for a shot but his effort flew well over the crossbar.However, United kept the momentum and Andreu was not far away with a lofted effort which just cleared the frame of Fox’s goal.But County soaked up all the pressure and killed the tie as a contest in the 78th minute when O’Brien set up Routis, who scored at the second attempt.The home side rubbed salt into the wound in stoppage time when Boyce teed the ball up nicely for O’Brien to roll the ball into the net for a debut goal. It was all-square in the 14th minute, though, when Tope Obadeyi drove into the box and cut the ball back for Tony Andreu, who volleyed past County goalkeeper Scott Fox.It only took a couple of minutes for County to restore their lead. They won a free kick on the edge of the area after Charlie Telfer was booked for a foul on Ryan Dow. Alex Schalk’s powerful shot was blocked by United keeper Cammy Bell but Paul Quinn was on hand to head in from close range.The foggy conditions got visibly worse as the half progressed with the away fans calling on the match official to call a halt to proceedings. Then two goals in as many minutes put County well in command.County made it 3-1 in the 28th minute when Routis got to the bye-line and his chip into the box was Tim Chow slotted the ball away from six yards. The home side opened up a three goal lead when Woods played the ball out to Boyce and he cut inside and fired a low drive into the far corner of the net.