Question

show that if gcd(a^2,b^2)=1then gcd(a,b)=1

Answer 1

Assume (a, b) has a gcd other than 1, say k.
Then (a^2, b^2) = (a * a, b * b) will have k * k or k^2 as its gcd. But since k^2 = 1, k = 1. So gcd(a, b) = 1.

Answer 2

okay makes sense