Problem

Topic 5: Polynomial and Other Equations
Determine the set of values of x for which the radical expression would produce a real number.
x+153

Select one:
a. {xx>15}
b. {xx15}
c. all real numbers
d. {xx>15}
PREVIOUS PAGE

Answer

Expert–verified
Hide Steps
Answer

The set of values of x for which the radical expression would produce a real number is all real numbers.

Steps

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 x+153 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 x+153 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 all real numbers.

link_gpt