Well, either you don't know what a social construct is or what real means. Or both.

Real does not mean true or false, it simply means that something exists. Say, the belief in God (or gods). It's very real, people kill and die for it, although we don't know whether it is true or false. Being an atheist I believe it to be false, but I can't prove it so, and even if I could it wouldn't be any less real for that.

A social construct is a common understanding or notion in a given society which is not an inevitable consequence of non-social factors. For example any notion of private property is a social construct, which is different among societies, and in some does not exist. Does it mean that it isn't real?