Question

Enrique says that the value of Vis a rational number for any positive, nonzero integer value of x. Select all of the values of x that could be used as counterexamples to show that Enrique's conjecture is false. 8.NS.1 x=1 x x=2 = x = 4 x = 5 X = 8 x=9 x=​

Answer 1

Enrique's conjecture that the square root of any positive, nonzero integer is a rational number can be disproved by showing counterexamples such as x = 2, x = 8, and others, where the square root is not rationals.

Step-by-step explanation:

The question seems to involve challenging a statement regarding rational numbers and their relationship to positive, nonzero integer values of x. Enrique's conjecture suggests that the square root of a positive integer is always a rational number, but this is not true. We can provide counterexamples to disprove this conjecture by selecting values of x for which the square root is known to be an irrational number.

A rational number can be expressed as the ratio of two integers (a fraction), where the denominator is not zero. For Enrique's conjecture to be false, we would need to find an integer value of x such that the square root of x cannot be expressed as a fraction. The classic example of an irrational number is the square root of 2. Therefore, x = 2 could be used as a counterexample. Similarly, the square roots of numbers like x = 8 and x = 9 are also irrational (although the square root of 9 is not). Therefore, these values of x serve as counterexamples to Enrique's statement.