 Hello and welcome to the session. Today I will help you with the following question. The question says proof that the following is irrational. 7 root 5. We know that a number is called irrational if it cannot be written in the form p upon q where nq are integers and q not equal to 0. This is the key idea for this question. Let's move on to the solution. The number given to us is 7 root 5. We have to show that this number is irrational. Let us assume that 7 root 5 is rational. Since it is rational so we can find co-prime and b where b is not equal to 0 such that 7 root 5 is equal to a upon b. Now this gives us root 5 is equal to a upon 7b. Now we know that 7a and b are integers and a upon 7b is rational so from here we get root 5 is also rational but this contradicts the fact root 5 is irrational. Hence our assumption that 7 root 5 is rational is not correct. Hence we get 7 root 5 is irrational. Hence proved. So hope you enjoyed the session. Have a good day.