Question

The slant height of a regular square pyramid is longer than its altitude.

Answer 1

Always

Because the slant length is the longest length when looking at the Pythagoras theorm

In this case the slant is y, with x and y as the height and base
y²=$x^{2}+y^{2}$

Hence y the slant is the sum of the height and and base and will always be larger 

Answer 2

Always.  If you were to take the cross section it would be a triangle.  If you draw the altitude in, you get a right triangle.  The hypotenuse is always longer than a side, the slant always has to be bigger.  See the attachment for more information.