 Hi students and welcome to the session. Let us discuss the following problem. Truth that the following are irrationals. Third part is 6 plus root 2. Let us now start the solution. First of all, let us assume that 6 plus root 2 is rational. Now put 6 plus root 2 equal to a upon b, where a and b are coplying such that b is not equal to 0. Let us recall that 2 numbers are coplying if they have no common factor other than 1. Now we know a upon b is equal to 6 plus root 2. This implies a upon b minus 6 is equal to root 2. This implies a minus 6 b upon b is equal to root 2. Now a and b are integers so a minus 6 b upon b must be rational. So we can write since a and b are integers a minus 6 b upon b is rational. Now a minus 6 b upon b is equal to root 2. So this implies root 2 is rational. This contradicts the fact that root 2 is irrational. This implies our assumption 6 plus root 2 is rational is wrong. Now we conclude that 6 plus root 2 is irrational. This is our required answer. This completes the session. Hope you enjoyed the session. Goodbye.