Simplifying 2 + 6 2 + 3 ?Is there anything else you can do to reduce it to something "nicer" other than multiplying it by 3 − 2 3 − 2 and get 6 − 2 + 18 − 12 ? The reason I think there's a nicer form is because the previous problem in the book was to simplify 3 + 2 2 − 3 − 2 2 , which simplifies nicely to ( 2 + 1 ) 2 − ( 2 − 1 ) 2 = 2.

Question

Simplifying                     2            +              6                            2            +              3            ?Is there anything else you can do to reduce it to something &quot;nicer&quot; other than multiplying it by                               3                −                  2                                      3                −                  2                     and get       6    −  2  +      18    −      12  ? The reason I think there&#039;s a nicer form is because the previous problem in the book was to simplify       3    +    2          2        −      3    −    2          2      , which simplifies nicely to       (          2        +    1          )      2        −      (          2        −    1          )      2        =  2.

Macie Melton · Accepted Answer

You are correct. Multiply by the conjugate which is       2    −      3  After multiplying by the conjugate we have             2      −              6            +              12            −              18                    −      1       which gives   −  2  +      6    −      12    +      18  . The only further simplification is as follows: Simplify       12   and       18   and we have   −  2  +      6    −  2      3    +  3      2

bsmart36 · Accepted Answer

Well, you could note that      6    −  2  +      18    −      12    =  −  2  +      6    (  1  −      2    +      3    )But beyond that, it doesn&#039;t look any better.

Answered question

Answer & Explanation

New Questions in Pre-Algebra