After winning the toss on a beautiful sunny day of the first ever day/night test match in England, Root and Cook lead the way for the hosts with brilliant hundreds.
Cook will return on day two 153 not out, while Root made a brilliant 136 against a West Indies' attack which offered very little throughout the first day with the pink ball.
The visitors took early wickets but Cook and Root then steadied the ship
Root's perfect first day of the series started well when he won the toss on a sunny day in Birmingham and chose to bat first with Mark Stoneman making his debut for the hosts.
The visitors though did start well with the ball when they reduced the hosts to 39-2 when Kemar Roach bowled Stoneman for eight and Miguel Cummins, who was making his debut for the visitors, removed Tom Westley for eight.
After the early wickets, the hosts needed their two best batsmen to steady the ship and that's exactly what they did as they saw the team to lunch without losing anymore wickets.
Cook went to lunch 50 not out, while Root ended the session on 40 not out as the hosts ended the first session on 108-2.
Root brought up his 13th test century as captain and vice-captain took their partnership past 150
After lunch, Cook and Root showed their true class as they managed to bat out the the full session without losing a wicket with the visitors not bowling well at all.
The pair took their partnership past the 150 mark as Root brought up his 13th test century before the end of the session.
At the end of the second session then, Cook was 85 not out, while Root ended the session 103 as the hosts reached 215-2 at tea.
Cook brought up his own century in the final session and will look to go big on day two
After tea, Cook didn't take long to bring up his own century as the pair took their partnership past the 200 mark.
The visitors were desperate to break the partnership and it took a brilliant delivery from Roach to end it on 248 when he removed Root for 136.
Dawid Malan, therefore, joined Cook at the crease in need of runs and the pair managed to see the hosts to the close without losing any more wickets.
During their unbeaten half-century partnership, Cook went past his 150 as the hosts ended day one on 348-3 with Cook 153 not and Malan 28 not out, with both batsmen looking for more runs tomorrow.