Question 357881
First find the length of the diagonal of one square face using the Pythagorean theorem.
Then use the diagonal as one leg of a right triangle with another side of the cube as the other leg and the hypotenuse will be the corner-to-corner diagonal you're after.
{{{D[1]^2=s^2+s^2}}}
{{{D[1]^2=2s^2}}}
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{{{D[1]^2+s^2=D[cc]^2}}}
{{{2s^2+s^2=D[cc]^2}}}
{{{D[cc]^2=3s^2}}}
{{{highlight(D[cc]=sqrt(3)*s)}}}