squarerootof2irrational
Square Root of 2 Irrational
Proof:
Suppose 2**(1/2)=a/b [hcf(a, b)=1][b>1]
a**2=2b**2
=> b|a**2
For some p, p|b, then p|a**2, so p|a
Hence hcf(a, b)>=p>1
Square Root of 2 Irrational
Proof:
Suppose 2**(1/2)=a/b [hcf(a, b)=1][b>1]
a**2=2b**2
=> b|a**2
For some p, p|b, then p|a**2, so p|a
Hence hcf(a, b)>=p>1