Let G=Kn1​,n2​,⋯,nt​​ be a complete t-partite graph on
n=∑i=1t​ni​ vertices. The distance between vertices i and j in
G, denoted by dij​ is defined to be the length of the shortest path
between i and j. The squared distance matrix Δ(G) of G is the
n×n matrix with (i,j)th entry equal to 0 if i=j and equal to
dij2​ if iî€ =j. We define the squared distance energy EΔ​(G)
of G to be the sum of the absolute values of its eigenvalues. We determine
the inertia of Δ(G) and compute the squared distance energy
EΔ​(G). More precisely, we prove that if ni​≥2 for 1≤i≤t, then EΔ​(G)=8(n−t) and if h=∣{i:ni​=1}∣≥1, then
8(n−t)+2(h−1)≤EΔ​(G)<8(n−t)+2h. Furthermore, we show that
for a fixed value of n and t, both the spectral radius of the squared
distance matrix and the squared distance energy of complete t-partite graphs
on n vertices are maximal for complete split graph Sn,t​ and minimal for
Tur{\'a}n graph Tn,t​