 Hi and welcome to the session. I am Priyanka and I am going to help you with the following question which says classify the following numbers as rational or irrational. Now these are the five parts to the question which are given to us and we need to tell them whether they are rational or irrational. So if we know that what are rational and irrational numbers we can easily classify them. Irrational numbers are those numbers which are non terminating non veckering decimals. That means they do not end and also the points after the decimal do not repeat. So and the vice versa is the rational numbers which are terminating decimals. So rational numbers are terminating decimals or it can be in the form of people by q where q is not equal to 0. Right? So the knowledge of what are rational number and irrational number and rational numbers are the key idea we are going to use in order to proceed on with our solution. So let us start with our solution. Now the first part is given to us as 2 minus root 5. Now we know that root 5 is an irrational number so therefore 2 minus root 5 will also be irrational number. So the answer to the first part is that it is an irrational number. Proceeding on to the next one. Now the number which is given to us is 3 plus root 23 in bracket minus root 23. So let us proceed on firstly opening the bracket that will be 3 plus under root 23 minus root 23. Root 23 will get cancelled to each other and we are left with 3. So it is a rational number because 3 can also be written as 3 by 1 where 1 is not equal to 0. So it is in the form of p by q where q is not equal to 0. So it satisfies the condition of being rational. Right? So this completes the second part. Proceeding on to the third part. 2 root 7 divided by 7 root 7. Now root 7 will get cancelled out with each other and we are left with 2 by 7 which is in the form of p by q where q that is the denominator is not equal to 0. So therefore we can write that 2 by 2 root 7 by 7 root 7 is a rational number. Proceeding on to the fourth part. We are given 1 by root 2. Now we know that root 2 is an irrational number. So therefore 1 by root 2 is an irrational number. Proceeding on to the last and final part. Section given to us is. Now again, i's value is an irrational value. So it is an irrational number basically. So anything multiplied by an irrational number will lead to an irrational number only. So 2 pi is an irrational number itself. So the answer to the last and final part is also irrational. So this completes the entire question which was given to us. I hope you liked the session. Just remember what are irrational and rational numbers and you can classify any number given to you according to the definitions and conditions known to you. I hope you enjoyed the session. Bye for now.