Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

"number between 17 and 18, and has a rational square root" Is there even one? They all keep coming up irrational for me

share|improve this question
2  
It would be more intruiging to know how you found the irrational ones. –  Tom Collinge Apr 28 at 12:28

3 Answers 3

Hint: Can you think of a rational number between $\sqrt{17}$ and $\sqrt{18}$?

share|improve this answer
2  
Perhaps to make it a little easier to see how to construct it: you want to form a number $ \ \frac{p^2}{q^2} \ $ , $ \ p \ $ and $ \ q \ $ being integers and with the numerator and denominator relatively prime, that is between $ \ 17^2 \ = \ 289 \ $ and $ \ 18^2 \ = \ 324 \ $ . –  RecklessReckoner Apr 27 at 19:24
3  
We can also use continued fractions. $\sqrt{17}=[4;\overline{8}]$ while $\sqrt{18}=[4,\overline{4,8}]$. Hence the "simplest" answer is $[4;5]=4\frac{1}{5}=4.2$. –  vadim123 Apr 27 at 19:27
7  
You can be as simple-minded as you like. Try $4.1$, $4.2$, $4.3$, etc., squaring each one, till you find one of the squares to lie between $17$ and $18$. In case you jumped over the interval $\langle17,18\rangle$, you could work on varying the second decimal place. –  Lubin Apr 27 at 19:58
    
@vadim123: Wouldn't the simplest answer be $[4,\overline{6,8}] = 2\sqrt{13/3}$? –  Eric Towers Apr 27 at 20:16
3  
@EricTowers, that is indeed simple, but alas not rational. –  vadim123 Apr 27 at 21:40

I like the positive root of $x^2 - x - \frac{217745}{16384}$.

share|improve this answer
    
Any particular reason? –  vonbrand Apr 28 at 10:45
    
It's as good as any other? –  orion Apr 28 at 11:29
2  
It is an irrational liking. –  Eric Towers Apr 28 at 13:04

"Is there even one?" Yes – there are infinitely many. (Exercise: Why?)

Hint: Guess the square root, not the number between 17 and 18.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.