not sure just how sloppy you are being with the parentheses, You might mean
√2+√(2+2cos4x)
or
√(2+√(2+2cos4x))
either way it's kinda sloppy
first step is probably to see what cos4x reduces to
2cosx=√2+√2+2cos4x
4 answers
2cosx
2cosx
√2+√2+2cos4x=2cosx