Simplifying a radical with complex fractionsSo I understand to simplify this: − 3 2 t 4 | 1 2 t 3 | 1 4 t 6 − 1 I can just multiply − 3 2 t 4 | 1 2 t 3 | 1 4 t 6 − 1 ⋅ 2 t 4 2 t 4 and get − 3 t 1 4 t 6 − 1 But how do you simplify further getting rid of the complex fraction inside the radical?

Question

Simplifying a radical with complex fractionsSo I understand to simplify this:                    −        3                    2                  t          4                                    |                    1                  2                      t            3                                      |                              1                      4                          t              6                                      −        1            I can just multiply                    −        3                    2                  t          4                                    |                    1                  2                      t            3                                      |                              1                      4                          t              6                                      −        1              ⋅            2              t        4                    2              t        4            and get            −      3              t                        1                      4                          t              6                                      −        1            But how do you simplify further getting rid of the complex fraction inside the radical?

haingear8v · Accepted Answer

−        3                    2                  t          4                                    |                    1                  2                      t            3                                      |                              1                      4                          t              6                                      −        1                        4              t        6                    4              t        6             first step will be to get rid of the fraction inside the radical. Note that              4              t        6              =      |    2      t    3        |                                −          3                          2                      t            4                                      |            2              t        3                    |                            |                    1                  2                      t            3                                      |                    1        −        4                  t          6                                1      −      4              t        6                    1      −      4              t        6             Then we get the radical outside of the numerator.                              −          3                          2                      t            4                                      |            2              t        3                    |                    1        −        4                  t          6                                    |                    1                  2                      t            3                                      |            (      1      −      4              t        6            )                          |            2              t        3                    |                            |            2              t        3                    |             Now I am taking on what you did in the first step. I think it is best to attack the messiest parts first.                              −          3                          2                      t            4                              (      4              t        6            )              1        −        4                  t          6                            (      1      −      4              t        6            )                    −      6              t        2                    1        −        4                  t          6                            (      1      −      4              t        6            )

gaiaecologicaq2 · Accepted Answer

−              3                                      2                              t                4                                                                        |                              1                                  2                                      t                    3                                                              |                                                      1                                  4                                      t                    6                                                              −              1                                                          =                                            −              3                                      2                              t                4                                                                        |                              1                                  2                                      t                    3                                                              |                                                                        1                  −                  4                                      t                    6                                                                    4                                      t                    6                                                                                                                        =                                            −              3                                      2                              t                4                                                                        |                              1                                  2                                      t                    3                                                              |                                                      1                −                4                                  t                  6                                                            4                                  t                  6                                                                                                      =                                            −              3                                      2                              t                4                                                                        1                              2                                                      |                    t                    |                                    3                                                                                    1                −                4                                  t                  6                                                            2                                  |                                t                                                      |                                    3                                                                                                      =                                            −              3                                      2                              t                4                                                                        1              −              4                              t                6                                                    4                              t                6                                                                                      =                                                            −                3                                            2                                  t                  4                                                      ×            4                          t              6                                            1            −            4                          t              6                                                                        =        −                              6                          t              2                                            1            −            4                          t              6                                      .