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Math Help - evaluating radicals

  1. #1
    Senior Member
    Joined
    Oct 2008
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    323

    evaluating radicals

    simplify and state restrictions on the variable
    a)(4+squareroot2)(5-squareroot8)
    b)2squareroot5+squareroot5
    c)3squareroot7-5squareroot7
    d)squareroot35/squareoot7
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  2. #2
    Newbie
    Joined
    Oct 2008
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    1) I don't know how to make it pretty, so I hope this works: First foil it:
    (4+sqrt(2))(5-sqrt(8))
    (4)(5) - 4sqrt(8) + 5sqrt(2) - sqrt(2)sqrt(8)

    Now you need to simplify sqrt(8) and sqrt(8)sqrt(2)

    This is how I do it: Take sqrt(8) and break it into it's factors, so you have:

    sqrt(8)=sqrt(2*4)=sqrt(2)*sqrt(4)=2*sqrt(2)

    Make sense? So if you do that we have:

    20 - 4*2*sqrt(2) + 5sqrt(2) - sqrt(16)

    Now you can just simplify:

    16 - 3sqrt(2)

    2) This one is a cinch:

    2sqrt(5) + sqrt(5) = 3sqrt(5)

    Do you see why?

    3) This is the same as 2.

    4) You need to break sqrt(35) into it's factors:

    sqrt(35) = sqrt(5*7) = sqrt(5)sqrt(7)

    Now we have:

    sqrt(35)/sqrt(7) = sqrt(5)sqrt(7)/sqrt(7) = sqrt(5)

    The two sqrt(7)s just cancel out.
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