 Hello and welcome to the session. I am Asha and I am going to help you solve the following question which says evaluate root over 3 plus root over 2 raised to the power 6 minus root over 3 minus root over 2 raised to the power 6. So let us begin with the solution and we have to evaluate the value of root over 3 plus root over 2 raised to the power 6 minus root over 3 minus root over 2 raised to the power 6. So let x is equal to root 3 and y is equal to root over 2. So this expression can further written as x plus y raised to the power 6 minus x minus y raised to the power 6. Now applying binomial theorem on both these terms it can further written as 6 c0 x raised to the power 6 into y raised to the power 0 plus 6 c1 x raised to the power 5 into y raised to the power 1 plus 6 c2 x raised to the power 4 into y raised to the power 2 plus 6 c3 x raised to the power 3 y raised to the power 3 plus 6 c4 x raised to the power 2 into y raise to the power 4 plus 6 c5 x raise to the power 1 into y raise to the power 5 plus 6 c6 x raise to the power 0 into y raise to the power 6 minus, now we will expand x minus y raise to the power 6 with the help of binomial theorem, so we have 6 c0 x raise to the power 6 into minus y raise to the power 0 plus 6 c1 x raise to the power 5 into minus y raise to the power 1 plus 6 c2 x raise to the power 4 into minus y raise to the power 2 plus 6 c3 x raise to the power 3 into minus y raise to the power 3 plus 6C4 x raise to the power 2 into minus y raise to the power 4 plus 6C5 x raise to the power 1 into minus y raise to the power 5 plus 6C6 x raise to the power 0 into minus y raise to the power 6. So, this is further equal to x raise to the power 6 plus 6C1 c1 is 6 x raised to the power 5 into y plus 6 c2 is 15 x raised to the power 4 into y square 6 c2 is 20 so we have 20 x cube y cube plus 15 x square y raised to the power 4 plus 6 x raised to the power 5 plus y raised to the power 6 and we have minus sign plus into minus is minus so we have minus x raised to the power 6 now on simplifying this we have minus 6 x raised to the power 5 into y and minus into minus is plus so we have plus 6 x raised to the power 5 into y now on simplifying this we get 15 x raised to the power 4 into y square plus into minus is minus so we have minus 15 x raised to the power 4 into y square on simplifying this we get minus 20 x cube y cube and minus into minus is plus so we have plus 20 x cube y cube on simplifying this we have plus 15 x square y raised to the power 4 which is minus 15 x square y raised to the power 4 and simplifying this we get plus 6 x into y raised to the power 5 minus y raised to the power 6 now x raised to the power 6 cancels out with x raised to the power 6 15 x raised to the power 4 minus 15 x raised to the power 4 into y square and 15 x square y raised to the power 4 minus 15 x square y raised to the power 4 and y raised to the power 6 minus y raised to the power 6 so this is equal to 6 plus 6 is 12 x raised to the power 5 into y in 20 plus 20 is 40 x cube y cube and 6 x raised to the power 5 sorry 6 x into y raised to the power 5 plus 6 x into y raised to the power 5 is 12 x into y raised to the power 5. So now we are substituting 3 equal to root over 3 and y is equal to root over 2 in this expression we can further write it as 12 to root over 3 raised to the power 5 into root over 2 plus 40 into root over 3 whole cube into root over 2 whole cube plus 12 times of root over 3 into root over 2 raised to the power 5. This is further equal to 12 into 3 into 3 into root over 6 plus 40 into 3 into 2 into root over 6 plus 12 into 2 into 2 into root over 6. So this is further equal to root over 6 now 12 9's are 108 plus 40 into 6 is 240 plus 12 4's are 48 which is further equal to root over 3 into 396 that's when evaluating we get the answer as 396 root over 6. So this completes the session hope you enjoyed it take care and have a good day.