Logitech Z906 to Hitachi smart tv

[goodfella55]

Hey there, i was just wondering if someone could help me this, trying to connect my 5.1 logitech Z906 surround sound speakers to my Hitachi 50inch Smart TV via RCA. Only problem is, i noticed there's not many options for outputs on the back of my TV, i don't know much about this, but most of the options of the back of my TV are inputs i think... I've connected the back of the subwoofer to the TV like you're supposed to, but the back of my TV's RCA connectors says input, there are no outputs. The only output thing i can see on the back of my TV is an optical output thing, does that mean i need to get an RCA to optical output connector? Any help will be great thank you! <3

 

[goodfella55]

https/www.amazon.co.uk/d/Home-Audio-Video-Accessories/Digital-Optical-Coaxial-Toslink-Converter/B009ZR7IB8/ref=sr_1_3?ie=UTF8&qid=1490196144&sr=8-3&keywords=RCA+to+optical+output+cable

Should i buy that item and try it?