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\sqrt{\sqrt{\sqrt{256}}}+\sqrt{4}
Calculate 4 to the power of 4 and get 256.
\sqrt{\sqrt{16}}+\sqrt{4}
Calculate the square root of 256 and get 16.
\sqrt{4}+\sqrt{4}
Calculate the square root of 16 and get 4.
2+\sqrt{4}
Calculate the square root of 4 and get 2.
2+2
Calculate the square root of 4 and get 2.
4
Add 2 and 2 to get 4.