To find the integer that \( \frac{9}{4} \) is close to the square root of, we first approximate \( \frac{9}{4} \):
\[ \frac{9}{4} = 2.25 \]
Now, we need to find an integer \( n \) such that \( \sqrt{n} \) is close to \( 2.25 \). To do this, we can square \( 2.25 \):
\[ (2.25)^2 = 5.0625 \]
Since \( n \) must be an integer, we check nearby integers, \( 5 \) and \( 6 \):
\[ \sqrt{5} \approx 2.236 \quad \text{and} \quad \sqrt{6} \approx 2.449 \]
The square root of \( 5 \) (approximately \( 2.236 \)) is closer to \( 2.25 \) than the square root of \( 6 \) (approximately \( 2.449 \)).
Thus, the integer that \( \frac{9}{4} \) is close to the square root of is:
\[ \boxed{5} \]
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