Ah feck. In future, I shall be more careful...
Edit: In the words of H.H.Munro
"A little inaccuracy sometimes saves a world of explanation."
Right so, the third square root may be greater than 1, but for every increase above 1 in that, there is double the decrease in the sum of the other two square roots, so the greater the value of the third square root, the lower the value overall.
I doubt that counts as a proof though..