Yes, it's correct to say 'What's your exact height?', but this seems a little formal - like something you might be asked at a medical examination, for example. In everyday conversation, we tend to say 'How tall are you?'. You could add 'exactly', as in 'Exactly how tall ARE you?' or 'How tall ARE you, exactly?'. We'd usually stress the verb here, to show that you already know more or less how tall the person is and now want an exact figure.

In conversation, people commonly say it like this. - He's one seventy six. (in BrE - 1m 76cm) - He's six (feet) nine and a half. (in AmE - 6' 9 1/2'")

Why not to say "She is 1.76 m tall"? 1.74m as you like