Adiagonal of a cube measures 30 inches. the diagonal of a face measures 600 square rooted inches. in inches, what is the length of an edge of the cube? round the answer to the nearest tenth. how many? inches

The diagonal of a cube is the square root of 3x^2, where x is a side lengthThe three dimensional diagonal is the counterpart to the two dimensional hypotenuse found in a right triangle...mathematically a three dimension diagonal can be found with an extension of the Pythagorean Theorem adapted to three dimensions...

d^2=x^2+y^2+z^2  but since we are dealing with a cube, x=y=z=s where s is a side lenght...

d^2=3s^2  and we are told that the diagonal is 30 in. so

3s^2=30^2

3s^2=900

s^2=300

s=√300

s=10√3 in.  exact

s≈17.3 in.  (to the nearest tenth of an inch)