Find the root of $$ \sqrt[5]{-3125} $$. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $$ \sqrt[5]{-3125}=\square $$ (Simplify your answer.) B. The root is not a real number.

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UpStudy AI · Accepted Answer

We start with the expression:
$$
\sqrt[5]{-3125}
$$

Since the index $$5$$ is odd, the $$5$$th root of a negative number is also negative. In other words, we have:
$$
\sqrt[5]{-3125} = -\sqrt[5]{3125}
$$

Next, we simplify $$\sqrt[5]{3125}$$. Notice that:
$$
3125 = 5^5
$$

Thus, we can write:
$$
\sqrt[5]{3125} = \sqrt[5]{5^5} = 5
$$

Substituting this back, we get:
$$
\sqrt[5]{-3125} = -5
$$

So, the correct choice is:

A. $$\sqrt[5]{-3125}=-5$$
The root of $$ \sqrt[5]{-3125} $$ is $$-5$$.

Find the root of \( \sqrt[5]{-3125} \). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( \sqrt[5]{-3125}=\square \) (Simplify your answer.) B. The root is not a real number.

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