To find the integer that is close to the square of \( \frac{9}{4} \), we first need to calculate \( \left(\frac{9}{4}\right)^2 \).
\[ \left(\frac{9}{4}\right)^2 = \frac{9^2}{4^2} = \frac{81}{16} \]
Next, we can convert \( \frac{81}{16} \) into a decimal for clarity:
\[ \frac{81}{16} = 5.0625 \]
Thus, \( \left(\frac{9}{4}\right)^2 \) is approximately \( 5.0625 \). The closest integer to \( 5.0625 \) is \( 5 \).
Therefore, \( \frac{9}{4} \) is close to the square root of \( 5 \).