Formal:
* 你愿意跟我约会吗? (nǐ yuàn yì gēn wǒ zuò yuē ma?) - This is the most formal way to ask someone out. It literally translates to "Are you willing to go on a date with me?".
* 你愿意和我一起出去吗? (nǐ yuàn yì hé wǒ yī qǐ chū qù ma?) - This is another formal way to ask. It means "Are you willing to go out with me?".
Informal:
* 你愿意跟我出去吗? (nǐ yuàn yì gēn wǒ chū qù ma?) - This is a less formal way to ask, more suitable for friends or people you know well. It means "Are you willing to go out with me?".
* 你愿意和我一起出去玩吗? (nǐ yuàn yì hé wǒ yī qǐ chū qù wán ma?) - This is even more casual and means "Are you willing to go out and have fun with me?".
* 你愿意做我的女朋友/男朋友吗? (nǐ yuàn yì zuò wǒ de nǚ péng yǒu/nán péng yǒu ma?) - This is a direct way to ask someone to be your girlfriend/boyfriend. It literally means "Are you willing to be my girlfriend/boyfriend?".
Note:
* You can use "你" (nǐ) or "您" (nín) when addressing someone. "您" is more formal.
* "跟" (gēn) and "和" (hé) both mean "with" but "跟" is slightly less formal.
* You can add "一起" (yī qǐ) meaning "together" after "和" (hé) or "跟" (gēn) for emphasis.
* "约会" (zuò yuē) is a specific word for a romantic date, while "出去" (chū qù) is more general and can be used for any outing.
Remember to choose the appropriate level of formality based on your relationship with the person you're asking. Good luck!