Topic 5: Polynomial and Other Equations
Determine the set of values of $x$ for which the radical expression would produce a real number.
\[
\sqrt[3]{x+15}
\]

Select one:
a. $\{x \mid x> -15\}$
b. $\{x \mid x \geq-15\}$
c. all real numbers
d. $\{x \mid x> 15\}$
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Step 1 ：The cube root of a number is defined for all real numbers. This is because any real number can be the cube of another real number. For example, the cube root of 8 is 2, and the cube root of -8 is -2.

Step 2 ：Therefore, the expression \(\sqrt[3]{x+15}\) is defined for all real numbers \(x\) such that \(x+15\) is a real number.

Step 3 ：Since the sum of two real numbers is always a real number, \(x+15\) is a real number for all real numbers \(x\).

Step 4 ：Therefore, the expression \(\sqrt[3]{x+15}\) is defined for all real numbers \(x\).

Step 5 ：The set of values of \(x\) for which the radical expression would produce a real number is \(\boxed{\text{all real numbers}}\).