Hi there

I was just wondering if you might be able to help me with this question:

Show that there is no rational number 's' such that s^2 = 3

thanks

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- Nov 2nd 2008, 01:42 PMdaaavorational number analysis
Hi there

I was just wondering if you might be able to help me with this question:

Show that there is no rational number 's' such that s^2 = 3

thanks - Nov 2nd 2008, 01:53 PMThePerfectHacker
Write $\displaystyle s=a/b$ where $\displaystyle a,b>1$. Then $\displaystyle a^2 = 3b^2$. Factor $\displaystyle a$ into primes and $\displaystyle b$ into primes. The exponents of the primes of $\displaystyle a^2$ will all be even similarly with $\displaystyle b$. However, $\displaystyle 3b^2$ will make one of the elements (i.e. $\displaystyle 3$) to be odd. And therefore the two sides do not match up. An impossibility.