What is the length of the line segment connecting the two most distant vertices of a 1 inch cube?

Find the square root of (1^2 + 1^2), which is the diagonal of one side of the cube.

= 1.4 inches

Then find the square root of (1.4^2 + 1^2), which is the length of the line segment connecting the two most distant vertices.

= square root of (1.96 + 1)
= square root of 2.96
= 1.72 inches