 Hello friends, so in this question, it's given to simplify 3 plus root 6 under root and sorry divided by 5 root 3 minus 2 root 12 minus root 32 plus root 50. So, that's a complex looking expression we need to simplify hence the word simplify. So, now if you see in the denominator there are multiple search and different search and underneath the root all the numbers are unequal. So, let us try to first of all simplify the denominator. So, if you see denominator, what is denominator? Denominator is 5 root 3. So, let me write it as D 5 root 3 minus 2 root 12 minus root 32 plus root 50. So, we can reduce them how? So, 5 root 3 minus 2 root 12 can be written as 2 square into 3, isn't it? And then root 32 can be written as 2 to the power 4 into 2, 16 into 2, 32 and root 50 can be written as 5 squared into 2, isn't it? Now further simplification will lead to 5 root 3 minus 2 into 2 root 3, isn't it? Minus 2 square into 2 plus 5 into, sorry this will be root 2 and 5 root 2, why? I will take one example and explain. So, for example, 2 to the power 4 into 2 is nothing but 2 to the power 4 into 2 whole to the power half right now. So, hence the value will be 2 to the power 4 by 2 into 2 to the power half, which is 2 to the power 2 into square root of 2, which is 4 root 2. So, I am just giving one example of simplification here, rest you can find out yourself, is it okay? So, what is it now? So, it is 5 root 3 minus 4 root 3 minus 4 root 2 plus 5 root 2. So, if you simplify, you will get root 3 5 root 3 minus 4 root 3 is root 3 and 5 root 2 minus 4 root 2 is plus root 2. So, this is the denominator. So, the given expression is reduced to 3 plus root 6 divided by root 3 plus root 2 and now you have to rationalize the denominator to simplify it further and you know that rationalization means multiplication by its conjugate. So, root 3 minus root 2 root 2 and here it is root 3 minus root 2 again because I divided by root 3 minus root 2, I have to multiply by root 3 minus root 2 and let us now open the brackets. So, it is 3 root 3 and it is minus 3 root 2 then root of 6 into 3 is root 18 and minus root of 6 into 2 is root of 12 isn't it divided by root 3 square minus root 2 square a square minus b square form. Now, you can simplify the numerator further it is 3 root 3 minus 3 root 2 and root 18 can be written as 3 square into 2 and 12 can be written as 2 square into 3 and divided by 3 minus 2 right. So, if you see it is nothing but 3 root 3 minus 3 root 2 plus 3 root 2 isn't it plus 3 root 2 I 3 square will come out of the root will become 3 this 3 square will come out of the root becomes 3 into root 2 and this is minus 2 root 3 right and divided by 1. So, hence minus 3 root 2 plus 3 root 2 goes and 3 root 2 minus 2 root 3 is nothing but root 3. So, can you see such a complex looking expression is reduced to only root 3 beautiful isn't it beautiful. So, that is how guys you need to solve or simplify a complex looking serred into a very simple looking serred.