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\sqrt{15-\sqrt{32+\sqrt{25-9}}}
Calculate the square root of 81 and get 9.
\sqrt{15-\sqrt{32+\sqrt{16}}}
Subtract 9 from 25 to get 16.
\sqrt{15-\sqrt{32+4}}
Calculate the square root of 16 and get 4.
\sqrt{15-\sqrt{36}}
Add 32 and 4 to get 36.
\sqrt{15-6}
Calculate the square root of 36 and get 6.
\sqrt{9}
Subtract 6 from 15 to get 9.
3
Calculate the square root of 9 and get 3.