 Hi students and welcome to the session. Let us discuss the following question. Truth that 3 plus 2 root 5 is irrational. First of all let us understand 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 idea to solve the given question. Remember, irrational numbers cannot be written in the form p upon q. Let us now start with the solution. First of all let us assume that 3 plus 2 root 5 is rational. 3 plus 2 root 5 equal to a upon b such that b is not equal to 0. Let us recall that co-prime numbers are those numbers which have no common factor other than 1. Now 3 plus 2 root 5 is equal to a upon b implies 2 root 5 is equal to a upon b minus 3. Now this implies root 5 is equal to a minus 3 b upon b. This further implies root 5 is equal to a minus 3 b upon 2 b. Now since a and b are integers this implies a minus 3 b upon 2 b is rational. So we can write a minus 3 b upon 2 b is rational. Now we know a minus 3 b upon 2 b is equal to root 5. Root 5 is also rational but this contradicts the fact that root 5 is irrational. Our assumption 3 plus 2 root 5 is rational is incorrect. So we conclude that 3 plus 2 root 5 is irrational. So this completes the session. Hope you understood the session. Goodbye.