Question

proove √2 is irrational​

Answer 1

hey dude !!!!

assume that √2 is a rational number..

√2= p/q ( where p and q are co prime and p≠q)

√2q=p

squaring on both side by 2

2q²= p²

2 is a factor of p²

2 is also a factor of p

know assume that p²= (2k)²

2q²=4k²

q²=2k²

therefore ,

2 is a factor of q²

2 is a factor of q

but we know that p and q are rational number as well as co prime ... there our supposition of assuming √2 is a rational number is wrong ...

So, √2 is an irrational number ....

hope this helps you