is it possible to travel from Shanghai to Zhuhai by train and how expensive is it?

There is no direct train running from Shanghai to Zhuhai. The best way is by air.

Thanks Cindy, wouldn't it be possible to take the fast train someplace close an change to another train? Is air travel expensive?

For trains, you can take a train to reach Guangzhou and then take bullet trains for Zhuhai. From Shanghai to Guangzhou, it costs you about 15 to 22 hours.
For the air travel, if you book at a good time, you can may get a discout, so that the ticket price may be cheap. It is hard to tell you the exact price. You can find the fare information on https://www.travelchinaguide.com/china-flights/

By train, you can take a fast train at Shanghai South Railway Station to Guangzhou first. Upon arrival at Guangzhou Railway Station, you can go to the nearby Provincial Bus Station to take a direct long-distance bus to Zhuhai.

Generally, air fare is much more expensive than train tickets. But travel by train is time-consuming.