How do I express 14/(3-√2) in the form of b+c√d?I don't really understand the method to express a surd. Can anyone help me with this question? I really want more ideas on how to solve it, maybe there is one I may understand well. TY

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How do I express 14/(3-√2) in the form of b+c√d?I don&#039;t really understand the method to express a surd. Can anyone help me with this question? I really want more ideas on how to solve it, maybe there is one I may understand well. TY

vard6vv · Accepted Answer

It&#039;s called rationalizing the denominator. This website actually has an example similar to your problem.                              14                      3            −                          2                                                          =                              14            (            3            +                          2                        )                                (            3            −                          2                        )            (            3            +                          2                        )                                                            =                              42            +            14                          2                                7                                                  =        6        +        2                  2

Nylah Burnett · Accepted Answer

Q    [      2    ] is a field (with the usual definitions of   + and   ⋅).What that means is that you can add, subtract, multiply, and divide two numbers of the type   a  +  b      2   and you&#039;ll get another number of that type.For your specific problem, first notice that   (  c  +  d      2    )  (  c  −  d      2    )  =      c    2    −  2      d    2   is just a rational number (it is also of the form   a  +  b      2  , where   b  =  0).So then we have the idea that if we want to get a number of the form   c  +  d      2   out of the denominator, we can just multiply it by   c  −  d      2   so that it becomes a regular rational number.Let&#039;s try it:      14          3      −              2              =      14          3      −              2              (  1  )  =      14          3      −              2                  (                  3        +                  2                            3        +                  2                      )    =            42      +      14              2              7    =  6  +  2      2

How do I express 14/(3-√2) in the form of b+c√d? I

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