Proving a number is a perfect square when all prime exponents are even

[chaotixmonjuish]

n=p₁^r₁...p_k^r_k

In order for p to be a perfect square, r must be even. Therefore

n=p₁^2h₁...p_k^2h_k

taking the square root of both sides I'm just left with

n=p₁^h₁...p_k^h_k

Does this work as a proof that n is a perfect square if r is even? It's a homework problem and I'm not sure if this is sufficient or correct at all.

 

[Dick]

If the p's are distinct primes, it's true the r's must be even for n to be a perfect square, but you haven't proved it. You haven't even stated the problem coherently. What's p?