Question

prove that root 2 is a irrational number.. with any tricky method..

Answer 1

Let us assume √2 is a rational number than exists two co-prime numbers a and b Such that.

√2=a/b

√2b=a

squaring both sides

(√2b)^2=(a) ^2
2b=a^2

let a=2k (K is any integer)

2b^2=4k^2
b.^2=2k^2
Therefore our assumption was wrong
√2 is irrational number