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how to prove root2 is irrational ?
 

Asked by kasagee1971 3rd April 2015, 2:07 PM
Answered by Expert
Answer:

l e t space u s space a s s u m e space square root of 2 space i s space a n space i r r a t i o n a l space n u m b e r. square root of 2 space equals space a over b space left parenthesis a space a n d space b space a r e space c o minus p r i m e right parenthesis square root of 2 b space equals space a space 2 b squared space equals space a squared b squared space equals space a squared over 2 s o comma space 2 space d i v i d e s space a squared comma space s o space 2 space a l s o space d i v i d e s space a s u p p o s e comma a space equals space 2 c a to the power of 2 space end exponent equals space 4 c squared 2 b to the power of 2 space space end exponent equals space 4 c squared space left parenthesis a squared space equals space 2 b squared right parenthesis b to the power of 2 space end exponent equals space 2 c squared c to the power of 2 space end exponent equals space b squared over 2 2 space d i v i d e s space b squared comma space s o space 2 space a l s o space d i v i d e s space b h e n c e space comma a space a n d space b space h a v e space a t l e a s t space 2 space a s space a space c o m m o n space f a c t o space b u t space i t space w a s a space s t a t e d space b e f o r e t h a t space a space space a n d space b space a r e space c o minus p r i m e left parenthesis n o space c o m m o n space f a c t o r right parenthesis t h i s space c o n t r i d a c t s space o u r space a s s u m p t i o n space t h a t space square root of 2 space i s space r a t i o n a l. h e n c e space square root of 2 space space i s space i r r a t i o n a l

Answered by Expert 6th April 2015, 4:54 PM
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