1. ## rational 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

2. Originally Posted by daaavo
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
Write $s=a/b$ where $a,b>1$. Then $a^2 = 3b^2$. Factor $a$ into primes and $b$ into primes. The exponents of the primes of $a^2$ will all be even similarly with $b$. However, $3b^2$ will make one of the elements (i.e. $3$) to be odd. And therefore the two sides do not match up. An impossibility.