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Thread: Radical terms expression

  1. #1
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    Question Radical terms expression

    Good evening,

    I am learning maths from scratch with some online websites and PDFs, so my level is pretty low.

    I am stuck with this simple expression with radical terms:

    "Write 4/1 + √5 in simplest form.

    Solution
    Begin by finding the conjugate of the denominator by writing the denominator and changing the sign.

    So the conjugate of 1 +√5 is 1 − √5.

    Then multiply the fraction by 1 − √5/1 − √5


    4/1 + √5 X 1 − √5/1 − √5 =

    4 − 4√5/−4 =

    √5 − 1"

    What I am missing is the very result. How do you obtain √5 − 1 from 4 − 4√5/−4 = ? Can anybody please explain to me which rule I should apply to get it?

    Thank you very much in advance!

    Claudia
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  2. #2
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    Re: Radical terms expression

    $\dfrac{4}{1+\sqrt{5}} \cdot \dfrac{1-\sqrt{5}}{1-\sqrt{5}} = \dfrac{4(1-\sqrt{5})}{1-5} = \dfrac{4(1-\sqrt{5})}{-4} = -(1-\sqrt{5}) = \sqrt{5}-1$
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  3. #3
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    Re: Radical terms expression

    By the way, " 4/1 + √5" in its simplest form is " 4 + √5". What you meant was " 4/(1 + √5)".
    Thanks from topsquark
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  4. #4
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    Re: Radical terms expression

    Quote Originally Posted by skeeter View Post
    $\dfrac{4}{1+\sqrt{5}} \cdot \dfrac{1-\sqrt{5}}{1-\sqrt{5}} = \dfrac{4(1-\sqrt{5})}{1-5} = \dfrac{4(1-\sqrt{5})}{-4} = -(1-\sqrt{5}) = \sqrt{5}-1$

    Thanks a lot! you were much more helpful than the example on the book ^^'
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