 Hello and welcome to the session. I am Shashi and I am going to help you with the following question. Question is prove that the following are irrational. First part is 1 upon root 2. First upon let us know what are irrational numbers? Irrational numbers are those numbers which cannot be written in the form p upon q where p and q are integers and q is not equal to 0. This is the key area to solve a given question. Let us now start the solution. Let us assume that 1 upon root 2 is rational. Now put 1 upon root 2 equal to a upon b such that a and b are coplying and b is not equal to 0. Now 1 upon root 2 equal to a upon b implies root 2 is equal to b upon a. Now we know b and a are integers so b upon a must be rational so we can write b upon a is rational. Now b upon a is equal to root 2 so this implies root 2 is also rational but this contradicts the fact that root 2 is irrational so our assumption that 1 upon root 2 is rational is incorrect so we conclude that 1 upon root 2 is irrational. This is the session hope you understood the session take care and goodbye.