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\sqrt{6+3}-\sqrt[3]{29-\sqrt{4}}
Calculate \sqrt[4]{81} and get 3.
\sqrt{9}-\sqrt[3]{29-\sqrt{4}}
Add 6 and 3 to get 9.
3-\sqrt[3]{29-\sqrt{4}}
Calculate the square root of 9 and get 3.
3-\sqrt[3]{29-2}
Calculate the square root of 4 and get 2.
3-\sqrt[3]{27}
Subtract 2 from 29 to get 27.
3-3
Calculate \sqrt[3]{27} and get 3.
0
Subtract 3 from 3 to get 0.