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Math Help - Help on radicals!!!!!

  1. #1
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    Help on radicals!!!!!

    Please help me! can anyone teach me to answer radicals step by step?

    kindly click on the attachment

    I really need your help urgently! after understanding your lesson I have 30 more items of that remaining to answer


    thank you
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  2. #2
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    Quote Originally Posted by Aussieboy View Post
    Please help me! can anyone teach me to answer radicals step by step?...

    I really need your help urgently! after understanding your lesson I have 30 more items of that remaining to answer...
    Hello,

    please tell us what are you supposed to do with those terms!

    EB
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Aussieboy View Post
    Please help me! can anyone teach me to answer radicals step by step?

    kindly click on the attachment

    I really need your help urgently! after understanding your lesson I have 30 more items of that remaining to answer


    thank you
    What exactly are you supposed to do with them? I can guess at the first one (if I'm reading it correctly)
    \sqrt{\frac{3}{16}} = \frac{\sqrt{3}}{\sqrt{16}} = \frac{\sqrt{3}}{\sqrt{4^2}}  = \frac{\sqrt{3}}{4}

    2 - 5 are already in simplest form and

    6. \sqrt[4]{m^{2a}n^4} = \sqrt[4]{m^2a} \sqrt[4]{n^4} = n \sqrt[4]{m^{2a}}
    (Technically, since \sqrt[4]{x^2} = (x^2)^{1/4} = x^{2/4} = |x|^{1/2} = \sqrt{|x|} this last can also be written n \sqrt{|m|^a}. Similarly 4 can be written as \sqrt{2|xy|} and 5 as \sqrt{|a - 3b|}.)

    -Dan
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  4. #4
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    Quote Originally Posted by earboth View Post
    Hello,

    please tell us what are you supposed to do with those terms!

    EB
    Oh! I forgot, simplify please
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  5. #5
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    Quote Originally Posted by topsquark View Post
    What exactly are you supposed to do with them? I can guess at the first one (if I'm reading it correctly)
    \sqrt{\frac{3}{16}} = \frac{\sqrt{3}}{\sqrt{16}} = \frac{\sqrt{3}}{\sqrt{4^2}}  = \frac{\sqrt{3}}{4}

    2 - 5 are already in simplest form and

    6. \sqrt[4]{m^{2a}n^4} = \sqrt[4]{m^2a} \sqrt[4]{n^4} = n \sqrt[4]{m^{2a}}
    (Technically, since \sqrt[4]{x^2} = (x^2)^{1/4} = x^{2/4} = |x|^{1/2} = \sqrt{|x|} this last can also be written n \sqrt{|m|^a}. Similarly 4 can be written as \sqrt{2|xy|} and 5 as \sqrt{|a - 3b|}.)

    -Dan

    Kindly elaborate all the steps and how to get the rationalizing factor?
    try this other examples
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  6. #6
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    Quote Originally Posted by Aussieboy View Post
    Kindly elaborate all the steps and how to get the rationalizing factor?
    try this other examples
    Hello,

    I'm refering to the 2nd collection of problems (Radicals 2.doc)
    (By the way: Do us and yourself a favour and start a new thread if you have new and other problems to solve. Otherwise you risk that noboby will notice these new problems)

    to #1: This is in simplest form already.

    to #2:
    \sqrt[4]{81m^4}=\sqrt[4]{3^4 \cdot m^4}=3m

    to #3:
    \sqrt[4]{81a^2}=\sqrt{\sqrt{3^4 \cdot a^2}}=3 \cdot \sqrt{a}
    I used the property that \sqrt[4]{x}=\sqrt{\sqrt{x}}

    to #4:
    I assume that your problem reads:
    5(a+b) \cdot  \sqrt{a+b}

    You know that x = \sqrt{x^2},\ x>0

    5(a+b) \cdot  \sqrt{a+b}=5 \sqrt{(a+b)^2}  \cdot  \sqrt{a+b}= 5 \cdot \sqrt{(a+b)^3}

    EB
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