 Hello and welcome to the session. Let us discuss the following question which says show that 5 minus 2 root 3 is an irrational number. Let's move on to its solution. Here we need to show that 5 minus 2 root 3 is an irrational number. So we will show this using contradiction. So first of all let us assume to contrary that 5 minus 2 root 3 is rational. Now if 5 minus 2 root 3 is rational then we can find co-prime numbers a and b where b is not equal to 0 such that 5 minus 2 root 3 is equal to a upon b. Therefore we will get 5 minus a upon b will be equal to 2 root 3. This implies 5 upon 2 minus a upon 2 b will be equal to root 3 that is root 3 will be equal to 5 b minus a upon 2 b. Now a and b are integers so this implies that 5 b minus a upon 2 b is rational. So this implies root 3 is also rational because 5 minus a upon 2 b which is rational is equal to root 3 so that means root 3 is also rational. But we already know that root 3 is irrational so that means this is a contradiction because root 3 is irrational thus assumption that 5 minus 2 root 3 is rational is wrong therefore we get that 5 minus 2 root 3 is irrational. So here we have proved that 5 minus 2 root 3 is irrational with this we finish this session hope you must have enjoyed it. Goodbye take care and have a nice day.