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\sqrt{45+\sqrt{13+\sqrt{8+1}}}
Calculate the square root of 1 and get 1.
\sqrt{45+\sqrt{13+\sqrt{9}}}
Add 8 and 1 to get 9.
\sqrt{45+\sqrt{13+3}}
Calculate the square root of 9 and get 3.
\sqrt{45+\sqrt{16}}
Add 13 and 3 to get 16.
\sqrt{45+4}
Calculate the square root of 16 and get 4.
\sqrt{49}
Add 45 and 4 to get 49.
7
Calculate the square root of 49 and get 7.