Question

determine whether the conjecture is true or false. if false, provide a counterexample.
#13 the square root of a perfect square is always a whole number. * 1 point
choose

if the statement above is false, provide a counterexample.
your answer

#14 all even numbers are composite. * 1 point
choose

Explanation:

Step1: Recall perfect - square definition

A perfect square is a number that can be written as the square of an integer. Let \(n = m^2\), where \(m\) is an integer. Then \(\sqrt{n}=\sqrt{m^2}=|m|\), and \(|m|\) is a whole number. So the statement "The square root of a perfect square is always a whole number" is true.

Step2: Recall composite - number definition

A composite number is a positive integer that has at least one positive divisor other than one or itself. The number 2 is an even number. But the factors of 2 are 1 and 2 only. So 2 is a prime number, not a composite number. Thus, the statement "All even numbers are composite" is false. The counter - example is 2.

Answer:

#13: True
#14: False, counter - example: 2