1 Given:
hoose the correct value(s) of from the list above so that is
4.1.1 Rational
4.1.2 Irrational
4.1.3 Non - real
4.1.4 Integer

To find the values of that fit each condition, we can evaluate the expression based on the provided values of .

First additional information:
To determine rational or irrational outputs of the expression, remember that a square root results in a rational number if the radicand (the value under the square root) yields a perfect square. Thus, for in the denominator, the resulting fraction must simplify to a square of a rational number. For example, gives us , leading to , which is rational.

Second additional information:
For non-real numbers, we must find values that make negative, resulting in a negative denominator. Among the provided values, gives , making the expression non-real because you cannot take the square root of a negative number in the realm of real numbers! So, for non-real outcomes, is a fitting choice.