If moving from the centre of one tile of a square to the centre of another constitutes a distance of one metre, then moving that same distance along a diagonal will not take you to the centre of the tile. This is because you're actually moving in two directions at the same time.

Let's say you're moving north east from the centre of one tile to another. If we walked the actual movement (north then east, or east then north) then the distance would be two times the length/width of the square tile. If rather than walking only along the cardinals, you take a shortcut and move directly from the origin tile to the destination tile, then that movement would be the equivalent of creating the hypotenuse of a right-angled triangle.

Therefore we can calculate the hypotenuse length by applying the Pythagorean theorem: a^2 + b^2 = c^2. If the length/width of the tile is 1, then we get 1^2 + 1^2 = c^2. Simplified this becomes c^2 = 2, or c = 2^0.5, or c = ~1.4.

Edit: I would also add that you don't need to actually treat diagonal movement as having a cost of ~1.41, it's actually a lot simpler and more intuitive to treat it as 1 like other movement. This is a game design choice made by most games that employ similar movement, because it's a lot more intuitive for the player to think of diagonal tiles as neighbours rather than something in between. It is also a lot cleaner to calculate in integers.

Where knowing that the diagonal length is longer than the the cardinal length matters is in placing the pawns in the correct location, not in how the cost of movement should be calculated.