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Math Help - A few Radical Problems

  1. #1
    Junior Member
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    A few Radical Problems

    Sorry guys ... just when I think I have the hang of these I have a few that jump out at me and make me start questioning what the heck I am doing.

    My first problem is to mulitply and simplify assuming all variables in a radicand represent positive real numbers. I made the checks because I am not able to create the great square root symbols you can make.

    √6x^3 * √4x^2


    Second Problem is to add or subtract as indicated:I am not sure how to get this one to type correctly so I will say it looks like an exponent above and before the square root symbol. so I will type it above
    3 3
    √27x^4 + √xy^6


    Third one I would think how many I have done of these I would have gotten this one correct. No laughing please!!

    it says to express each number in terms of i and simplify if possible.
    √-63
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  2. #2
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    Quote Originally Posted by kbryant05

    √6x^3 * √4x^2
    Note that,
    \sqrt{6x^3}=\sqrt{6x\cdot x^2}=\sqrt{6x}\cdot \sqrt{x^2}=x\sqrt{6x}
    Also note that,
    \sqrt{4x^2}=\sqrt{4}\cdot\sqrt{x^2}=2x
    Therefore,
    (2x)\cdot (x\sqrt{6x})=2x^2\sqrt{6x}

    Quote Originally Posted by kbryant05
    3 3
    √27x^4 + √xy^6
    Note that,
    \sqrt[3]{27x^4}=\sqrt[3]{27\cdot x^3\cdot x}=\sqrt[3]{27}\cdot \sqrt[3]{x^3}\sqrt[3]{x}=3x\sqrt[3]{x}
    Also that,
    \sqrt[3]{xy^6}=\sqrt[3]{y^6}\sqrt[3]{x}=y^2\sqrt[3]{x}
    When added,
    3x\sqrt[3]{x}+y^2\sqrt[3]{x}=(3x+y^2)\sqrt[3]{x}
    Quote Originally Posted by kbryant05[/tex
    √-63
    This is a trick I always told my classmates. Do the problem,
    \sqrt{63} then worry about the negative.
    You have,
    \sqrt{63}=\sqrt{9\cdot 7}=\sqrt{9}\cdot \sqrt{7}
    Thus,
    3\sqrt{7}
    Now introduce the "i" because the number was negative.
    3i\sqrt{7}

    This is my 13th post!!!
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  3. #3
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    Thumbs up Brilliant!!!

    Thank you!!! I feel like an idiot just when I get so close I miss something. I started to do the FOIL method on the first one and went way beyond where I should have been going. Thanks for making it look so easy!!
    I really appreciate the help you guys give!!!
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