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## 'Rationals Between' printed from http://nrich.maths.org/

I am searching for fractions with values between $\sqrt{56}$ and
$\sqrt{58}$. I'm told there are an infinite number of
possibilities...

Find some fractions with small denominators,
say less than $10$ or $20$.

Have you found any denominators which won't yield a fraction
between $\sqrt{56}$ and $\sqrt{58}$?

Send us any examples you find of denominators which don't work, and
a justification that all other denominators will work!