Reduction to absurdity: Assuming that root number 2, root number 3 and root number 50% are arithmetic progression, then:

2 times root number 3 = root number 2+ root number 5.

Square both sides to get 2.5 = root sign 10. How can rational numbers be equal to irrational numbers? This is a contradiction.

So the hypothesis is not established, and the original proposition is proved.

After getting "2.5 = root number 10", both sides can be squared to get 6.25 = 10.