A perfect square is a number that can be expressed as the square of an integer. To determine if 35 is a perfect square, we will check the integers whose squares are close to 35.
Calculating the squares of integers:
Since
Additionally, we can also check the prime factorization of 35:
The prime factorization shows that 35 does not have pairs of prime factors; a perfect square must have all prime factors raised to an even power.
Thus, since 35 is not the square of any integer, we conclude that 35 is not a perfect square.