\begin{tabular}{l} Berween which two positive integers do the follawing irrational number lies? \\ \( \sqrt{11} \) \\ \hline\end{tabular}

To find the two positive integers between which the irrational number \( \sqrt{11} \) lies, we can start by calculating the square roots of the integers surrounding 11. 1. **Identify the integers**: The integers we need to consider are 3 and 4, since \( 3^2 = 9 \) and \( 4^2 = 16 \). This means \( 9 < 11 < 16 \). 2. **Calculate the square roots**: - \( \sqrt{9} = 3 \) - \( \sqrt{16} = 4 \) Since \( 9 < 11 < 16 \), we can conclude that: \[ 3 < \sqrt{11} < 4 \] Thus, the two positive integers between which \( \sqrt{11} \) lies are **3 and 4**.