Ajuice container is a square prism with base edge length 4 inches. when an 8-inch straw is inserted into the container as shown, exactly 1 inch remains outside the container. the length of ab is inches, to the nearest inch. (enter only the number.)

Assuming AB is the height because we are given it has a square base with 4 by 4

so draw a diagram ( see attachment)
given tha the 8 inch straw ha 1 inch sticking out, the diagonal is 7

use pythagorean theorem twice since 2 right triangles
a^2+b^2=c^2
4^2+4^2=c^2
16+16=c^2
32=c^2
sqrt both sides
4√2=c
the bottom diagonal is 4√2

bottom^2+height^2=7^2
(4√2)^2+(AB)^2=7^2
32+(AB)^2=47
minus 32 both sides
(AB)^2=15
sqrt both sides
AB=√15
if AB is the height