The diagonal of the face of a cube is equal to 9√3. Find the diagonal of the cube.

Thank you! :)

We have that  2s^2 = d^2      where s is the side and d is the diagonal......so we have

2s^2  = (9√3)^2

2s^2 = 243   divide by 2 on both sides

s^2 = 243/2   take the square root of both sides

So  s = √(243/2)

And the diagonal of a cube is given by

√(3s^2)  =  √[3(243/2)] = √(243*1.5) = about 19.09  units