How can I write the numbers 5 and 7 as some sequence of operations on three 9s?

I want to make the numbers 1,2,...,9 using exactly three copies of the number 9 and the following actions: addition, subtraction, multiplication, division, squaring, taking square roots, and other action.

How can we make the numbers 5 or 7?

For example, we can make the below numbers using exactly three copies of the number 9.

  • 1=9×99
  • 2=9+99
  • 3=9×99
  • 4=99+9
  • 5=?
  • 6=9+99
  • 7=?
  • 8=999
  • 9=9+99.

Now, how can we make the numbers 5 and 7?

Answer

5=9!99,7=9!+99

Attribution
Source : Link , Question Author : elham , Answer Author : fuglede

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