Problem 130 (difficulty: 4/10)

Prove that

 (1)  \(\displaystyle \sqrt 3\) is irrational;      (2)  \(\displaystyle {\sqrt 2 \over \sqrt 3}\) is irrational;      (3)  \(\displaystyle {{{{\sqrt 2 + 1} \over 2} + 3} \over 4} + 5\) is irrational!

Give me another random problem!