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Math Help - rationalising the denominator

  1. #1
    Junior Member
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    rationalising the denominator question? who knows

    Given that (2+square root of 7)(4-square root of 7) = a + b(square root of 7)
    a) find the value of a and value of b

    b) given that 2+(square of 7) / 4+(square of 7) = c +d(square of 7) where c and d are rational numbers,

    find the value of c and value of d.

    ummmm..
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  2. #2
    Junior Member
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    Manchester
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    The first case involves multiplying out the brackets and then collecting like terms. You'll be able to collect terms with a factor of root 7.

    The second case involves multipling the fraction by 1 expressed as ( 4 - root 7) / (4 - root 7). The point being that the denomitor can be multiplied out to remove the surd.
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  3. #3
    MHF Contributor
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    Given that (2+square root of 7)(4-square root of 7) = a + b(square root of 7)
    a) find the value of a and value of b

    [2 +sqrt(7)]*[4 -sqrt(7)] = a +b[sqrt(7)]
    2*4 +2(-sqrt(7)) +sqrt(7)*4 +sqrt(7)*(-sqrt(7)) =
    8 -2sqrt(7) +4sqrt(7) -7 =
    1 +2sqrt(7) =
    So, a=1 and b=2 ---------answer.

    -----------------
    b) given that 2+(square of 7) / 4+(square of 7) = c +d(square of 7) where c and d are rational numbers, find the value of c and value of d.

    [2 +sqrt(7)] / [4 +sqrt(7)]
    Rationalize the denominator. Multiply both numerator and denominator by the conjugant of the denominator, which is [4 -sqrt(7)],
    = [2 +sqrt(7)]*[4 -sqrt(7)] / [4 +sqrt(7)]*[4 -sqrt(7)]
    = [8 +2sqrt(7) -7] / [16 -7]
    = [1 +2sqrt(7)] / 9
    = (1/9) +(2/9)sqrt(7)
    So, c = 1/9, and d = 2/9 ----------answer.
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