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.