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\sqrt{41-\sqrt{21+\sqrt{19-3}}}
Calculate the square root of 9 and get 3.
\sqrt{41-\sqrt{21+\sqrt{16}}}
Subtract 3 from 19 to get 16.
\sqrt{41-\sqrt{21+4}}
Calculate the square root of 16 and get 4.
\sqrt{41-\sqrt{25}}
Add 21 and 4 to get 25.
\sqrt{41-5}
Calculate the square root of 25 and get 5.
\sqrt{36}
Subtract 5 from 41 to get 36.
6
Calculate the square root of 36 and get 6.