What is the square root of 337?

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Answer 1 · 2016-05-13T18:24:29

$sqrt(337) ~~ 18.35755975$ is not simplifiable since $337$ is prime.

$337$ is prime - it has no positive factors apart from $1$ and itself.

As a result, $sqrt(337)$ is not simplifiable.

It is an irrational number which when squared (multiplied by itself) gives you $337$ . Its value is approximately $18.35755975$ .

Since it is irrational, its decimal representation neither terminates nor recurs.

It has a continued fraction expansion which does repeat, namely:

$sqrt(337) = [18;bar(2,1,3,1,11,2,4,1,3,3,1,4,2,11,1,3,1,2,36)]$

$=18+1/(2+1/(1+1/(3+1/(1+1/(11+1/(2+1/(4+1/(1+...))))))))$

To construct rational approximations for $sqrt(337)$ you can truncate this continued fraction.

For example:

$sqrt(337) ~~ [18;2,1,3,1] = 18+1/(2+1/(1+1/(3+1/1))) = 257/14 ~~ 18.357$