What is the square root of 200?

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  • 8 months ago

    I assume you do have a calculator so we will approximate sqrt 200.  First let f(x) = sqrt(x).  We need to find a value a at which we can easily take the square root.  The square root of 196 is 14 and 196 is close to 200 so it will suffice.  We will take the 3rd degree Taylor polynomial to approximate sqrt(200).  For 3rd degree we find f(x) ~ f(a) + f’(x-a)+(f’’(x-a)^2)/2!.  Plug in number and f(sqrt200) ~ 14 + 1/28 -1/(sqrt(196^3)) = 14.0355.  This, sqrt of 200 is approximately 14.0355.  Note: the 2nd degree Taylor polynomial approximation would’ve have produced a better estimate of sqrt(200).

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  • David
    Lv 7
    8 months ago

    It is an irrational number which is 10 times the square root of 2

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  • sepia
    Lv 7
    8 months ago

    The square root of 200 is 14.14213562

    • 8 months agoReport

      WRONG! It's an irrational number, you need to say "approximately"

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  • 8 months ago

    The square root of 200 is 14.1421356

    • 8 months agoReport

      WRONG! It's an irrational number, you need to say "approximately"

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  • 8 months ago

    The square root of 200 is simplified into a mixed radical form 10 root 2.

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  • TomV
    Lv 7
    8 months ago

    200 = 2*100

    √200 = √2 * √100

     = 10√2 ≈ 14.14

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  • Anonymous
    8 months ago

    14.14213562 or 10√2

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  • Como
    Lv 7
    8 months ago

    :-

    In mathematical problems will usually be expressed as :-

    √ 200 = √ ( 100 x 2 ) = 10 √2

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  • 8 months ago

    sqrt(200) = sqrt(100)*sqrt(2) = 10*1.414 = 14.14

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  • Lôn
    Lv 7
    8 months ago

    14.14 to 2 dp......

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