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\sqrt{125-\sqrt{64}+\sqrt[3]{64}}
Calculate 5 to the power of 3 and get 125.
\sqrt{125-8+\sqrt[3]{64}}
Calculate the square root of 64 and get 8.
\sqrt{117+\sqrt[3]{64}}
Subtract 8 from 125 to get 117.
\sqrt{117+4}
Calculate \sqrt[3]{64} and get 4.
\sqrt{121}
Add 117 and 4 to get 121.
11
Calculate the square root of 121 and get 11.