To find the integer that \( \frac{9}{4} \) is close to the square root of, we can start by squaring \( \frac{9}{4} \).
\[ \left( \frac{9}{4} \right)^2 = \frac{81}{16} \]
Next, we can convert \( \frac{81}{16} \) to a decimal to determine its approximate value.
\[ \frac{81}{16} = 5.0625 \]
This means that \( \frac{9}{4} \) is close to the square root of 5.0625. To find the nearest integer, we examine the integers 5 and 6:
- \( \sqrt{5} \approx 2.236 \)
- \( \sqrt{6} \approx 2.449 \)
We find that \( \sqrt{5.0625} \) is equal to \( \frac{9}{4} \):
\[ \sqrt{5.0625} = \frac{9}{4} \]
Thus, we can conclude that \( \frac{9}{4} \) is close to the square root of the integer \( 5 \).
In summary, \( \frac{9}{4} \) is close to the square root of the integer \( \boxed{5} \).
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