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Math Help - Simplifying Radicals

  1. #1
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    Simplifying Radicals

    I'm trying to study Algebra on my own and need help with simplifying radicals (pre-algebra). I watched a video on khan academy and got confused. Could someone at least give 3-10 examples of simplifying radicals.

    1. 8\sqrt{}80

    2. 6\sqrt{}243

    3.5\sqrt{}99

    And more examples if possible
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  2. #2
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    if in doubt, break every number down to its prime factors (this isn't the cleverest way, but will always work...i think)



    you try one
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  3. #3
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    Quote Originally Posted by SpringFan25 View Post
    if in doubt, break every number down to its prime factors (this isn't the cleverest way, but will always work...i think)



    you try one
    Could you show me a few more examples ?

    And how did you get 2 to the second power ?
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  4. #4
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    Quote Originally Posted by luffy28 View Post
    Could you show me a few more examples ?
    And how did you get 2 to the second power ?
    You should understand that this is not a tutorial service. You are certainly welcome to post some of your own work on these problems so that we can help you understand how they work.
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  5. #5
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    edit didnt see previous post

    And how did you get 2 to the second power ?
    you need to be more specific about which 2^2 you are talking about.



    here is the second example, same method: break all numbers into prime factors.
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  6. #6
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    5\sqrt{}48

    5\sqrt{}2 \cdot 2 \cdot 2\cdot 2\cdot 3 \cdot
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  7. #7
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    Nobody is going to do your work - what do you understand about prime factors?
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  8. #8
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    when things are multiplies by each other under the square root sign, you can split them into seperate square roots:


    Can you simplify that some more?
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  9. #9
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    its good that you are watching khan academy videos but do you have a standard algebra 1 textbook? you need to read about radicals. the books have lots of step by step examples and problems. those videos are only extra help while reading and doing problems in an algebra textbook.

    you can get a used textbook on amazon for $5 us dollars.... just look at the older used copys. I used Ron Larson in class.
    Amazon.com: Elementary and Intermediate Algebra A Combined Course (9780618753543): Larson; Hostetler: Books

    you can also try ck12 algebra books. altho I have not personally read the algebra 1 book. I did read some of the the trig book and it was close to my textbook.
    CK12.ORG - FlexBooks
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  10. #10
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    5\sqrt{99}
    5\sqrt{9*11}
    5*3\sqrt{11}
    15\sqrt{11}
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  11. #11
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    Quote Originally Posted by ihavenonick View Post
    5\sqrt{99}
    5\sqrt{9*11}
    5*3\sqrt{11}
    15\sqrt{11}
    Very good!

    How about this one?
    \sqrt{14} \cdot \sqrt{35}

    -Dan
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  12. #12
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    Quote Originally Posted by luffy28 View Post

    And more examples if possible

    2\sqrt{338}=2\sqrt{169*2}=2*13\sqrt{2}=26\sqrt{2}

    sqrt{24}=sqrt{4*6}=2\sqrt{6}



    5\sqrt{44}
    You must transform radicand into product of numbers, one of these must be a number of 2nd root:
    our radical is 44; 44=11*4; 4=2^2; so:
    5\sqrt{44}=5\sqrt{11}*sqrt{4}
    sqrt{4}=2, `cause 2^2=4; so:
    5\sqrt{11}*sqrt{4}=5\sqrt{11}*2=5*2\sqrt{11}=10\sq rt{11}

    Will have a question - turn to me in the future
    Last edited by ihavenonick; April 30th 2011 at 07:01 AM.
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  13. #13
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    Quote Originally Posted by topsquark View Post
    Very good!

    How about this one?
    \sqrt{14} \cdot \sqrt{35}

    -Dan
    sqrt{14}*sqrt{35}
    14=2*7; 35=5*7,so
    sqrt{14}=sqrt{2*7}=sqrt{2}*sqrt{7}
    sqrt{35}=sqrt{5*7}=sqrt{5}*sqrt{7}, so:
    sqrt{14}*sqrt{35}=sqrt{2}*sqrt{7}*sqrt{5}*sqrt{7}= (sqrt{7}*sqrt{7})(sqrt{2}*sqrt{5})=7*sqrt{5*2}=7\s qrt{10}
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