Answer
The root test is inconclusive.
Work Step by Step
To apply the root test, we have
$$
L=\lim _{k \rightarrow \infty} \sqrt[k]{a_{k}}=\lim _{k \rightarrow \infty} \sqrt[k]{(k/(k+10)^k)}\\
=\lim _{k \rightarrow \infty} \frac{k}{k+10}=1
$$
Hence the root test is inconclusive.
