Would it be weird to say this to my teacher?

Hello! I’m not Jewish but one of my teachers is. This year I’ve been trying to learn more about religions and I took a world religions intensive at the beginning of the school year. I only very recently learned what Rosh Hashanah was and I think it’s pretty cool and swag. I also learned about the phrase “L’shanah tovah tikatevu v’techatemu” and I think it’s honestly a really beautiful thing to say to someone cause of what it means. I’ve seen various different ways of shortening it, some people say that saying L’shanah tovah is sloppy and you’re just supposed to say shanah tovah, and I don’t know if it would be weird for be to say the whole thing/if it sounds too stuffy and formal. I also don’t want her to think I’m not trying to learn and I was too lazy to figure out the proper pronunciation for the whole thing if I shorten it. I also don’t know if I’m allowed to say this to a teacher? She doesn’t talk a ton about her religion but she wore a Hanukkah sweater last year and she’s told me she’s Jewish. Overall I think she’s pretty cool and awesome and I wanna wish her a happy year. I’ve seen a lot of different opinions and I don’t wanna screw up, if yall can let me know the most respectful way to go about this I would really appreciate it. If it matters I’m also a dude and she’s obviously a woman.

*woman not girl