I'm using the rounded height of Everest!
But supposing the highest mountain on earth had been a lot more than that.
What height would it have to be to make it unclimbable?
Or would some sort of specially adapted "space suit" have been developed specifically for climbers to make the top section climbable.
Gonna have to make assumptions about the terrain at the top of such a mountain. i.e not a very difficult technical section.