International Youth Math Challenge 2024: Problem C: Determine the numerical value of the following

Determine the numerical value of the following expression without the use of a calculator:
(√2+(3^2 )^(1/4)+∑_(m=1)^3▒(1/m!-√m) ).(2^log_2⁡8 +1/2^3 -∏_(k=1)^8▒(1+1/k) )