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algebra

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Radicals are so confusing. Can someone show me step by step please. Im lost

5/8+√7

  • algebra -

    The main point is to recall that (a-b)(a+b) = a^2-b^2

    So, if you want to get rid of roots in the denominator, multiply top and bottom by the "conjugate" expression

    (8+√7)(8-√7) = 8^2 - √7^2 = 64-7 = 57

    So,

    5/(8+√7) = 5(8-√7)/((8+√7)(8-√7))
    = 5(8-√7)/57
    = (40 - 5√7)/57

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