2  yokka vargamoolam ahetukamani anaku rajuvu ivvande 
 ikda  2  yokka vargamoolam ahetukam ani vairudhyam dwara rajuvu Pali .  mundhuga ,  akaraneeya sankhyalu  p  mariyu  q  puurnaamkaala choose  p / q  gaaa vraayaleni sankhyalu ani gurthunchukondi .  vairudhyam choose  2  yokka vargamoolam hetubaddhamainadani bhavinchandi ,  antey konni puurnaamkaala  p  mariyu  q  choose  sqrt(2) = p / q  ani ardham .  yea bhinnam taggina ruupamloe undani saadhaaranatanu kolpokunda oohinchandi ,  antey  p  mariyu  q  ummadi kaarakaalu ekv panchukolevu .  edaina puurnaamkam bhinnam atuvanti taggina ruupamloe vraayabadutundi kabaadi manam dheenini oohinchavachchu ,  kabaadi  sqrt(2) ki edaina hetubaddhamaina praatinidhyam vunte adi taggina ruupamloe okati unikini suchisthundi .  ippudu manam pai sameekaranam yokka remdu vaipulaa vargeekaristaamu 

2 = p^2 / q^2

 konni puurnaamkaala choose  p  mariyu  q  e sadarana kaarakaalanu panchukoledu .  ippudu pomdadaaniki  q^2 thoo guninchandi 

2 * q^2 = p^2

 edama chethi vaipu  2  karakam kaaranamgaa samaanamgaa untundani gamanimchamdi ,  kabaadi Kandla vaipu  p^2  kudaa alaage umtumdi .  deeni ardham  p  tappanisariga samaanamgaa vundali ,  lekapote  p^2  samaanamgaa undadhu .  kabaadi  p  konni puurnaamkam  x  choose  2 * x  gaaa vraayavachhu .  pai sameekaranamlo dheenini pratyaamnaayam cheestee ,  manaku labisthundhi 

2 * q^2 = (2 * x)^2 = 2^2 * x^2

 sameekaranam yokka remdu vaipulaa manam raddhu cheeyagala  2  karakam undani gamanimchamdi .  ila cheeyadam will manaku labisthundhi 

q^2 = 2 * x^2

 piena paerkonnadaanitoe samaanamaina vaadhana dwara ,  meemu  q  sari ani nirdhaarinchavachchu .  ayithe idi  p  mariyu  q  ummadi kaarakaalanu panchukoledane maa vuhaku viruddhamgaa Pali .  anevalla  sqrt(2)  hetubaddhamainadane maa praadhimika ooha thappu ,  dheenini meemu niroopinchaalanukuntun .