why root 2 is not a rational number
Asked by rkarim957 | 17th Mar, 2019, 07:41: PM
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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