merasional kan penyebut dari 1 +3 akar 2 per akar 3+ akar 5

[tex] \frac{1 + 3 \sqrt{2} }{ \sqrt{3} + \sqrt{5} } \times \frac{ \sqrt{3} - \sqrt{5} }{ \sqrt{3} - \sqrt{5} } = \frac{ \sqrt{3} - \sqrt{5} + 3 \sqrt{6} - 3 \sqrt{10} }{3 - 5} = - ( \frac{ \sqrt{3} - \sqrt{5} + 3 \sqrt{6} - 3 \sqrt{10} }{2} )[/tex]

1 + 3√2      √3 - √5        √3 - √5 + 3√6 - 3√10
----------  x  -----------  =  ---------------------------
√3 + √5      √3 - √5          √3(√3)  - √5(√5)

                                      √3 - √5 + 3 (√6 - √10)
                                  =  -----------------------------
                                               3 - 5

                                      √3 - √5 + 3(√6 - √10)
                                   = ----------------------------
                                               - 2