Answers

2016-04-23T10:53:45+05:30
For ex:- √2
=let us assume that √2 is an rational number.
=let a and b are two co-primes.

√2 is rational so

√2=a/b
√2b=a
squaring on both sides
so, 2b²=a²
b²=a²/2
so, 2 divides a² and 2
divides a
let, a = 2c

so, b²=(2c²)/2
b²=4c²/2
b²=2c²
b²/2=c²
so, 2 divides b² and 2
divides b

but according to the fact co-primes do not have the same factor i.e.., a and b have the factor 2

so, this contradicts our fact that √2 is rational.

so that √2is an irrational number
0