"number between 17 and 18, and has a rational square root" Is there even one? They all keep coming up irrational for me
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$\begingroup$Hint: Can you think of a rational number between $\sqrt{17}$ and $\sqrt{18}$?
$\endgroup$ 5 $\begingroup$I like the positive root of $x^2 - x - \frac{217745}{16384}$.
$\endgroup$ 3 $\begingroup$"Is there even one?" Yes – there are infinitely many. (Exercise: Why?)
Hint: Guess the square root, not the number between 17 and 18.
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