 Hello and welcome to the session. In this session, we will discuss the following question and the question says, simplified by rationalizing the denominator of each irrational number part A, 2 by root 7, part B, root 5 by root 7, part C, 3 divided by 2 into root 6, part D, 5 plus root 3, whole divided by root 3. Let's start the solution now. In part A, we are given 2 by root 7. Now we have to simplify this irrational number by rationalizing the denominator. For this, we will multiply both numerator and denominator by least possible irrational number such that the denominator becomes a rational number. So in this case, we multiply both numerator and denominator by root 7. So multiplying both numerator and denominator by root 7, we get the given irrational number 2 by root 7 becomes 2 by root 7 multiplied by root 7 divided by root 7, which is equal to 2 into root 7 divided by root 7 into root 7, which is equal to 7. So, after rationalizing the denominator, the given irrational number becomes 2 into root 7 divided by 7, which is the answer for the first part. Now in part B, we have the irrational number root 5 by root 7. We have to rationalize the denominator of this irrational number. First, we will look for the least possible irrational number, which when multiplied by the denominator, the denominator becomes a rational number. The least possible irrational number in this case is root 7. So we multiply both numerator and denominator by root 7. So multiplying both numerator and denominator by root 7, we get root 5 by root 7 becomes root 5 by root 7 into root 7 divided by root 7. Now this is equal to root 5 into root 7 is equal to root 35. So the numerator becomes under root 35 divided by root 7 into root 7, which is equal to 7. So the denominator is 7. So after rationalizing the denominator, the given irrational number becomes root 35 divided by root 7, which is our answer for part B. We now move on to part C. We are given the irrational number 3 divided by 2 into root 6. Since root 6 is the least possible irrational number, which when multiplied with the denominator, the denominator becomes a rational number. So we multiply both numerator and denominator by root 6. Multiplying numerator and denominator by root 6, we get 3 divided by 2 into root 6 becomes 3 by 2 into root 6 multiplied by root 6 divided by root 6. This is equal to 3 into root 6 divided by root 6 into root 6 becomes 6. So the denominator is 2 into 6. This is equal to 3 into root 6 divided by 12. Now 3 4 times is 12. So this is equal to root 6 by 4. So after rationalizing the denominator, the given irrational number becomes root 6 by 4, which is our answer for the part C. Now in part D, we are given the irrational number 5 plus root 3 whole divided by root 3. To rationalize the denominator, we multiply both numerator and denominator by root 3. So multiplying both numerator and denominator by root 3, we get 5 plus root 3 divided by root 3 becomes 5 plus root 3 by root 3 into root 3 divided by root 3 which is equal to root 3 into 5 plus root 3 the whole whole divided by root 3 into root 3. Now this is equal to the numerator becomes 5 into root 3 plus root 3 into root 3 which is equal to 3 whole divided by root 3 into root 3. So the denominator is 3. So after rationalizing the denominator, the given irrational number becomes 5 root 3 plus 3 whole divided by 3 which is the answer for part D. With this, we end our session. Hope you enjoyed the session.