# What is the square root of 200?

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

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• The square root of 200 is 14.14213562

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

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• The square root of 200 is 14.1421356

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

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

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• 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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• :-

In mathematical problems will usually be expressed as :-

√ 200 = √ ( 100 x 2 ) = 10 √2

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

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• 14.14 to 2 dp......

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