Question

where i hav done wrong!!
i m unable to find any mistake!!
right answer is 9 + 4√6 / 15

Answer 1

Sol : Hey , the mistake that you did was in rationalizing the denominator.To rationalize the denominator , we multiply  the numerator and denominator by the same rationalizing factor of denominator.But instead of multiplying the numerator by  ( 4√3 - 3√2 ) , you multiplied it by ( 4√3 - 5√2 ).

Here is your solution ,


       4√3 + 5√2
= ---------------------------
        √48 + √18

         4√3 + 5√2
= -----------------------------
         4√3 + 3√2

By multiplying the numerator and denominator by ( 4√3 - 3√2 ),

    ( 4√3 + 5√2 ) ( 4√3 - 3√2 )
=  -----------------------------------------
     ( 4√3 + 3√2 ) ( 4√3 - 3√2 )


   ( 4√3 x 4√3 ) - ( 4√3 x 3√2 ) + ( 5√2 x 4√3 ) - ( 5√2 x 3√2 )
= --------------------------------------------------------------------------------
                               ( 4√3)² - (3√2)²

       48 - 12√6 + 20√6 - 30
= -------------------------------------
                   48 - 18 

      18 + 8√6
= ------------------------
             30

     2 ( 9 + 4√6 )
= ------------------------
          30

= ( 9 + 4√6 ) / 15.

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