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Math Help - Finding the value of a square root

  1. #1
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    Finding the value of a square root

    What would be the quickest method to estimate (i.e to the nearest integer) the value of 3\sqrt{-89}?

    If 89 has a factor of 3 it wouldn't be too bad but given that its a prime this question seems a little difficult.

    thx
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by dumluck View Post
    What would be the quickest method to estimate (i.e to the nearest integer) the value of 3\sqrt{-89}?

    If 89 has a factor of 3 it wouldn't be too bad but given that its a prime this question seems a little difficult.

    thx
    3 \sqrt{-89}=3i \sqrt{89}=-3i \sqrt{10^2-11}

    ............. =- 30 i \sqrt{1+11/100} \approx 30 i (1-(11/100)(1/2)+..)

    CB
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  3. #3
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    For a really "rough" estimate:
    sqrt(100) = 10
    sqrt(81) = 9
    10 > sqrt(89) > 9 ; get my drift?
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  4. #4
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    Quote Originally Posted by Wilmer View Post
    For a really "rough" estimate:
    sqrt(100) = 10
    sqrt(81) = 9
    10 > sqrt(89) > 9 ; get my drift?
    Thanks Wilmer, that's the level I want to be at. However the answer is between -4 and -5?
    Last edited by dumluck; May 7th 2011 at 07:22 AM.
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  5. #5
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    Ok I think I have it 4.4.4 = 64 5.5.5 = 125 therefore it is between -4 and -5.
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by dumluck View Post
    Ok I think I have it 4.4.4 = 64 5.5.5 = 125 therefore it is between -4 and -5.
    I'm sorry but it is not between any real numbers it is imaginary. Alternatively you have posted something other than what you think you have.

    CB
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  7. #7
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    Quote Originally Posted by dumluck View Post
    Thanks Wilmer, that's the level I want to be at. However the answer is between -4 and -5?
    The fact that you wrote " 3\sqrt{-89}" and titled this "Finding the value of a square root" made it very difficult for people to figure out that you really wanted the cube root, \sqrt[3]{-89}.
    -4^3= -64 and -5^3= -125 so the cube root of -89 is between -4 and -5.
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