Question

find all real fifth roots of 32. if there are multiple answers, separate them with commas.
write your answers in simplified form.

Explanation:

Step1: Define the fifth root equation

Let $x$ be a real fifth root of 32, so $x^5 = 32$.

Step2: Rewrite 32 as a power of 2

$32 = 2^5$, so the equation becomes $x^5 = 2^5$.

Step3: Solve for real $x$

For real numbers, if $x^n = a^n$ and $n$ is odd, $x=a$. Here $n=5$ (odd), so $x=2$. There are no other real fifth roots because odd-indexed roots have exactly one real root for real numbers.

Answer:

2