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\sqrt{18+\sqrt{52-\sqrt{5+4}}}
Calculate the square root of 16 and get 4.
\sqrt{18+\sqrt{52-\sqrt{9}}}
Add 5 and 4 to get 9.
\sqrt{18+\sqrt{52-3}}
Calculate the square root of 9 and get 3.
\sqrt{18+\sqrt{49}}
Subtract 3 from 52 to get 49.
\sqrt{18+7}
Calculate the square root of 49 and get 7.
\sqrt{25}
Add 18 and 7 to get 25.
5
Calculate the square root of 25 and get 5.