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\sqrt{4+4\sqrt{4+5}}
Calculate the square root of 25 and get 5.
\sqrt{4+4\sqrt{9}}
Add 4 and 5 to get 9.
\sqrt{4+4\times 3}
Calculate the square root of 9 and get 3.
\sqrt{4+12}
Multiply 4 and 3 to get 12.
\sqrt{16}
Add 4 and 12 to get 16.
4
Calculate the square root of 16 and get 4.