Rationalise the denominator and simplify 3 2 − 4 3 2 + 4 Does someone have an idea how to work 3 2 − 4 3 2 + 4 by rationalising the denominator method and simplifying?

Question

Rationalise the denominator and simplify             3              2            −      4              3              2            +      4       Does someone have an idea how to work                     3                  2                −        4                    3                  2                +        4             by rationalising the denominator method and simplifying?

Marlee Norman · Accepted Answer

3                  2                −        4                    3                  2                +        4              ⋅                    3                  2                −        4                    3                  2                −        4              =  =                    18        −        24                  2                +        16                    (        3                  2                          )          2                −                  4          2                      =                    34        −        24                  2                            18        −        16              =                    2        (        17        −        12                  2                )            2        =  =  17  −  12      2    .

Yahir Crane · Accepted Answer

For problems like this, you need to multiply numerator and denominator by the denominator&#039;s conjugate. A conjugate is found by flipping the sign from positive to negative or negative to positive in a binomial. So, the denominator&#039;s conjugate in the above&#039;s equation is   3      2    −  4. Multiplying an irrational binomial by it&#039;s conjugate will rationalize it, as seen below:            3              2            −      4              3              2            +      4        ×            3              2            −      4              3              2            −      4      Multiply out the bottom and top            9      ×      2      −      12              2            −      12              2            +      16              9      ×      2      −      16        =            18      −      24              2            +      16              18      −      16        =            34      −      24              2              2    =  17  −  12      2

Rationalise the denominator and simplify 3 <msqrt> 2 </msqr

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