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\sqrt{22+\sqrt{7+\sqrt{2+2}}}
Calculate the square root of 4 and get 2.
\sqrt{22+\sqrt{7+\sqrt{4}}}
Add 2 and 2 to get 4.
\sqrt{22+\sqrt{7+2}}
Calculate the square root of 4 and get 2.
\sqrt{22+\sqrt{9}}
Add 7 and 2 to get 9.
\sqrt{22+3}
Calculate the square root of 9 and get 3.
\sqrt{25}
Add 22 and 3 to get 25.
5
Calculate the square root of 25 and get 5.