Question

Find the real solution(s) of the following equation.
\[p^3 = 125\]
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
\[p = 3\]
A
\[p = 3\]
(Choice B)
\[p = -3\]
B
\[p = -3\]
(Choice C)
\[p = 6\]
C
\[p = 6\]
(Choice D)
\[p = -6\]
D
\[p = -6\]
(Choice E) None of the above
E
None of the above

Answer 1

To find the real solution(s) of the equation

\[
p^3 = 125,
\]

we start by taking the cube root of both sides.

The cube root of 125 is

\[
\sqrt[3]{125} = 5.
\]

Thus, the equation

\[
p^3 = 125
\]

has the solution

\[
p = 5.
\]

Now, we review the choices provided:

- (Choice A) \(p = 3\) — This is not a solution.
- (Choice B) \(p = -3\) — This is not a solution.
- (Choice C) \(p = 6\) — This is not a solution.
- (Choice D) \(p = -6\) — This is not a solution.
- (Choice E) None of the above — This is the correct choice since \(p = 5\) is not listed.

Therefore, the correct answer is

\[
\text{(Choice E) None of the above.}
\]