command=lambda: root.quit()
This will call root.quit() and pass its result to the function.
That should be:
command=lambda: root.quit
              
tried suggestion , still not exiting when click button

thank for reply
import tkinter as tk
from tkinter import ttk
# root window
root = tk.Tk()
root.geometry('300x200')
root.resizable(False, False)
root.title('Button Demo')
# exit button
exit_button = ttk.Button(
    root,
    text='Exit',
    command = root.quit
exit_button.pack(
    ipadx=5,
    ipady=5,
    expand=True
root.mainloop()
as Cameron said.
However, your original code does work.
Were you running it from a Python prompt?
If yes, then root.mainloop() will finish and the prompt will return, but the window will remain because the tkinter module still has a reference to it. That’s not a problem when you’re running a script because you’ll be quitting the Python interpreter just afterwards, but you can close that window by using root.destroy() instead.
              
am using IDLE (Python 3-11 64-bit)
run in visual studio code , and it worked there
wonder what the problem is with IDLE , though it is simpler to use than VS code
thanks