"Intricate" sort of means technical, a little detail-oriented, a bit complex ( but not like nuclear physics abviously). An intricate answer to a question is one that is fairly thoroughly and detailed. Or you might say this "This new Airbus A-380 has a highly indricate wiring system (meaning complex)." Sophisticated just means refined. It's normally used with people "she's a sophisticated lady" meaning high caliber, maybe , but necessarily, highly educated. Smooth and polished in her appearance, speech, manners. Or a machine can be sophisticated. A 2016 Mercedes is a lot more sophisticated of a car than a 1932 Ford Medel A. But it's so in every respect. It's more generally true than saying simply that the car's motor is more sophisticated.

They're synonyms when they mean "complex" in the context of a device/machine/solution to a problem, but each of them has other meanings, which means that generally they're not interchangeable. - sophisticated can mean worldly, not naive, high-class, glamorous: "she's a very sophisticated person, always dresses and behaves impeccably" - intricate can mean very detailed, obscure, hard to understand, maze-like: "the network of tunnels is so intricate that it would be impossible to explore them without a map" "Complex" could be applied to both of the examples above "a complex person" and "a complex network of tunnels", but an important part of the meaning and subtext is lost or changed (a complex person refers to a difficult character, rather than a stylish one, and a complex network doesn't convey the "obscure" and "maze-y" meaning).

Good question. Intricate is complicated or complex. Sophisticated can be 1.) having a high sense of fashion or culture OR it can be 2.) complicated or complex. Example sentences: 1. Google's algorithm is very intricate. Many computer scientists have tried to understand it, but they could not. 2. The supermodel from Paris is sophisticated. Her clothes are elegant and very fashionable. 3. The race car has a sophisticated engine. It was designed by a group of experts. I hope this has helped you!