trig

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How can I get rid of the square roots in this fraction?

sqrt((2-sqrt3))/sqrt((2+sqrt3))

the answer is 2-sqrt3

but I don't know how they arrive at it.

  • trig -

    Multiply both the numerator and denominator by the conjugate, sqrt((2-sqrt3))
    Then
    sqrt(2-sqrt3)/sqrt(2+sqrt3)
    =sqrt(2-sqrt3)sqrt(2-sqrt3)/(sqrt(2+sqrt3)sqrt(2-sqrt3))
    =sqrt((2-sqrt3)²)/sqrt(2²-3)
    =(2-sqrt(3))/sqrt(4-1)
    =(2-sqrt(3))/sqrt(1)
    =2-sqrt(3)

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