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Math Help - Problem Solving #3

  1. #1
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    Problem Solving #3

    Are the two numbers
    square root of 3 + and square root of 11 and
    square root of 5 + square root of 8 equal? If not, which is larger?
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  2. #2
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    Use calculator.
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  3. #3
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    Quote Originally Posted by matgrl View Post
    Are the two numbers

    square root of 3 + and square root of 11 and
    square root of 5 + square root of 8 equal? If not, which is larger?
    Without knowing the background to this question, post #2 is all you can reasonably expect to get ....
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    I am not allowed to. I obviously know which one is bigger using a calculator. This is problem solving
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  5. #5
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    I know I need to set an equation making these vairbales equal to each other. Then I need to square this equation but this is all I know.
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    Hello, matgrl!

    \text{Are the two numbers }\sqrt{3} + \sqrt{11}\,\text{ and }\,\sqrt{5} + \sqrt{8}\,\text{ equal?}

    \text{If not, which is larger?}

    We have: . . . . \sqrt{3} + \sqrt{11} \quad[?]\quad \sqrt{5} + 2\sqrt{2}

    Square: . . 3 + 2\sqrt{33} + 11 \quad [?]\quad 5 + 4\sqrt{10} + 8

    . . . . . . . . . . . 1 + 2\sqrt{33} \quad [?] \quad 4\sqrt{10}

    Square: . 1 + 4\sqrt{33} + 132 \quad [?]\quad 160

    . . . . . . . . . . . . . . 4\sqrt{33} \quad[?]\quad 27

    Square: . . . . . . . . . 528 \quad[?]\quad 729


    Since 528 < 729, the original statement is: . \sqrt{3} + \sqrt{11} \;<\;\sqrt{5} + \sqrt{8}


    Last edited by Soroban; November 3rd 2010 at 08:22 AM.
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    This is great! Once again thank you
    I have a question on the way you did your square roots. How exactly does the 4 square root of 33 = 528? I am not sure how to do this...could you show me?
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  8. #8
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    Quote Originally Posted by matgrl View Post
    How exactly does the 4 square root of 33 = 528?
    Look again at what was done: 4SQRT(33) was squared;
    4 squared = 16; SQRT(33) squared = 33 : 16 * 33 = 528
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