 Hello friends welcome again to session on certs and today in this session We are going to learn the application of rationalization if you have not learned rationalization, I would suggest to go through the rationalization sessions and You would be able to understand the concept Now in this question it is given that root 2 is 1.414 And you have to find the value of 1 plus root 2 divided by 3 minus 2 root 2 to 3 places of Decimals, let us see how to use rationalization to solve this problem. So first of all, let's rationalize the given given third so 1 plus root 2 Divide by 3 minus 2 root 2. So what do we need to do? We need to multiply it with its conjugate and only the denominator so 1 plus root 2 Divide by 3 minus 2 root 2 can be multiplied by its conjugate, which is 3 plus 2 root 2 and Then the same thing has to be done on the numerator as well, right? So this is the final multiplication now And the numerator you can open the brackets and you can say 1 times 3 plus 1 times 2 root 2 plus root 2 times 3 plus root 2 times 2 root 2, right? The numerator is like that and the denominator simply is 3 square minus 2 root 2 square. Why? Because you know a plus b times a minus b is Equal to a square minus b square, right? So use that in the denominator. So in the numerator, what do I get? I get 3 plus 2 root 2 plus 3 root 2 plus 2 times root 2 times root 2 is 2 times 2 that is 4, right? And in the denominator guys, we get 9 minus 4 times 2 that is 8, right? So you see 2 root 2 square is 2 square into root 2 square So hence it is 4 into 2 hence 8, understood? Now so in the numerator what is What do we obtain? We obtain 3 plus 4 that is 7 plus 5 root 2 divided by 1 Isn't it? 7 plus 5 root 2 divided by 1. So hence now it's given 1 root 2 is 1.414 So it is 7 plus 5 into 1.414 You can do the calculations. You will get 7 plus 5 4s are 20 carry 2 5 1s are 5 so it's 7 5 4s are 20 again So 2 so 7.070 is the value and hence added 7 to it So you'll get 14.070 So hence this is how we obtained the value of the given sir the moment one of the values of Let's say one of these values were given so root 2 values were given was given and hence We could obtain the value of the complete complex looking sir Into in three places of decimal up to three places of decimal So this is one of the areas of application of application of rationalization application of rationalization Okay, so we'll take up another such question in the next session