How can you tell by drawing a factor tree whether or not a number is a square number?

A factor tree tells you the prime factorization. The prime factorization can indicate a square number. Square numbers have even pairs of prime factors. 2 x 2 x 3 x 3 is a square number. 5 x 5 x 5 x 5 x 7 x 7 x 7 x 7 is a square number.