Question

Determine if 35 is a perfect square, explaining why or why not. (1 point)

Answer 1

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:

- \( 5^2 = 25 \)
- \( 6^2 = 36 \)

Since \( 25 < 35 < 36 \), we see that 35 lies between the squares of 5 and 6. Therefore, there is no integer \( n \) such that \( n^2 = 35 \).

Additionally, we can also check the prime factorization of 35:
- \( 35 = 5 \times 7 \)

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.