why root 2 is not a rational number

Asked by rkarim957 | 17th Mar, 2019, 07:41: PM

Expert Answer:

let us consider √2 is a rational number .
 
Then we can write,  √2 = a / b    .............................(1)
 
where a and b are co-prime, i.e., there is no common factor between a and b .
 
By squaring both sides of eqn.(1),  we get,   a2 / b2  = 2   .................(2)
 
From eqn.(2), it appears b2,  which is an integer,  is a factor of a .
 
[  if a square of integr number x is divisible by integer y, i.e., x2 is divisible by y, then y is a factor of x ]
 
But we started with the assumption a is prime number.
 
We get into this contradiction because of our assumption √2 is a rational number.
 
Hence √2 is not a rational number. √2 is an  irrational number

Answered by Thiyagarajan K | 17th Mar, 2019, 09:58: PM

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