Between what two consecutive integers do $sqrt250$ lie?

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Answer 1 · 2015-10-21T23:17:58

Between $15$ and $16$

$15^2 = 225 < 250 < 256 = 16^2$

So

$15 = sqrt(225) < sqrt(250) < sqrt(256) = 16$

In fact

$sqrt(250) = [15; bar(1,4,3,3,4,1,30)]$

$= 15+1/(1+1/(4+1/(3+1/(3+1/(4+1/(1+1/(30+...)))))))$

$~~ 15.8113883$

Between what two consecutive integers do sqrt250sqrt250 lie?