Consider the given inequality,
![\sqrt[]{x}\leq11](https://img.qammunity.org/2023/formulas/mathematics/college/va86kt65iwdgu5vpc9iv2jq38z5y384dcu.png)
Note that a square root inequality is defined only if the 'x' is non-negative.

Now, squaring both sides will not affect the inequality as both sides are positive terms,
![\begin{gathered} (\sqrt[]{x})^2\leq11^2 \\ x\leq121 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/jyfjd2j53jil5uipudl78g0bbtjkd0sfv9.png)
Combining the two results,

Thus, the solution set to the inequality is the set of all real numbers from 0 to 121 .