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Math Help - surds

  1. #1
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    surds

    may i please have help solving with the following 2 equations:
    <br />
3b^3 \sqrt{20 a^3 b^2 c^5}<br />
    and
    \sqrt{3}(4+\sqrt{3}- \sqrt{15})
    Last edited by griffince; June 3rd 2009 at 03:35 PM. Reason: i type it wrong
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  2. #2
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    Quote Originally Posted by griffince View Post
    may i please have help with the following 2 equation:

     3b^3 square root 20a^3 b^2 C^5
    and
     square root 3(4+square root 3- square root 15)
    Don't understand what kind of help you need.
    But it looks as if you want to have the equations to look like this:


     3b^3 \sqrt{20 a^3 b^2 c^5}

    and

     \sqrt{3(4+ \sqrt{ 3} - \sqrt{15})}

    Is that the help you need?
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  3. #3
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    yes and to solve them
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  4. #4
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    Quote Originally Posted by griffince View Post
    may i please have help solving with the following 2 equations:
    <br />
3b^3 \sqrt{20 a^3 b^2 c^5}<br />
    and
    \sqrt{3}(4+\sqrt{3}- \sqrt{15})
    What you have are NOT equations. You only have an equation when you have an equals sign.

    I think you're asking to simplify these expressions.

    For the first one:

    3b^3\sqrt{20 a^3 b^2 c^5} = 3b^3\times\sqrt{20}\times\sqrt{a^3}\times\sqrt{b^2  }\times\sqrt{c^5}

     = 3b^3\times\sqrt{4\times 5}\times\sqrt{a^2\times a}\times b \times \sqrt{c^4\times c}

     = 3b^4 \times \sqrt{4}\times\sqrt{5}\times\sqrt{a^2}\times\sqrt{  a}\times \sqrt{c^4} \times \sqrt{c}

     = 3b^4 \times 2 \times \sqrt{5} \times a \times \sqrt{a} \times c^2 \times \sqrt{c}

     = 6ab^4c^2 \times \sqrt{5} \times \sqrt{a}\times \sqrt{c}

     = 6ab^4c^2\sqrt{5ac}



    The second one looks already simplified. You can't break up a surd over addition and subtraction (only multiplication and division) and there aren't any other common factors besides the 3.

    I think the only other ways it could be written are

    \sqrt{3}\sqrt{4 + \sqrt{3} - \sqrt{15}}

    or

    \sqrt{12 + 3\sqrt{3} - 3\sqrt{15}}.
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  5. #5
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    The OP's 2nd question is different than what has been discussed:
    \sqrt{3}(4+\sqrt{3}- \sqrt{15})

    Assuming that this is the actual question, to solve this you distribute the square root of 3:

    4\sqrt{3} + \sqrt{3}\sqrt{3} - \sqrt{3}\sqrt{15}

    4\sqrt{3} + 3 - \sqrt{45}

    4\sqrt{3} + 3 - 3\sqrt{5}

    3 + 4\sqrt{3} - 3\sqrt{5}


    01
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