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

1 answer

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:

  • 52=25
  • 62=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 n2=35.

Additionally, we can also check the prime factorization of 35:

  • 35=5×7

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.