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\sqrt{5+\sqrt{13+3}}
Calculate the square root of 9 and get 3.
\sqrt{5+\sqrt{16}}
Add 13 and 3 to get 16.
\sqrt{5+4}
Calculate the square root of 16 and get 4.
\sqrt{9}
Add 5 and 4 to get 9.
3
Calculate the square root of 9 and get 3.