Question

Suppose x is a real number and

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for some real number q. What conclusion can you draw from this about x?
a) x must be irrational.
b) x must be rational.
c) x could be rational or irrational.

Answer 1

x could be rational or irrational, depending on whether q is a perfect square or not.

Step-by-step explanation:

If x is a real number that satisfies the equation x = q1/2 for some real number q, we can conclude that x could be rational or irrational. This is because the square root of a real number can result in either a rational number (if q is a perfect square) or an irrational number (if q is not a perfect square). For example, if q = 4, then x = 2, which is rational. However, if q = 2, then x is the square root of 2, which is known to be irrational. Whether x is rational or irrational depends entirely on the nature of the value of q.

The conclusion that can be drawn about x from the given information is that x could be rational or irrational. The fact that x is a real number and q is a real number does not provide enough information to determine whether x must be rational or irrational. A real number can either be rational (can be expressed as a fraction) or irrational (cannot be expressed as a fraction).