To find the integer that \( \frac{9}{4} \) is close to the square root of, we first calculate the value of \( \frac{9}{4} \):
\[ \frac{9}{4} = 2.25 \]
Next, we want to find the integer \( n \) such that \( \sqrt{n} \) is close to \( 2.25 \). We can square \( 2.25 \) to find this integer:
\[ (2.25)^2 = 2.25 \times 2.25 = 5.0625 \]
Since \( 5.0625 \) is not an integer, we can look for the closest perfect squares to \( 5.0625 \). The perfect squares around this value are \( 4 \) (which is \( 2^2 \)) and \( 9 \) (which is \( 3^2 \)).
- The square root of \( 4 \) is \( 2 \), which is less than \( 2.25 \).
- The square root of \( 9 \) is \( 3 \), which is greater than \( 2.25 \).
Thus, the integer \( n \) that \( \frac{9}{4} \) is approximately the square root of is:
\[ \boxed{5} \]
In summary, \( \frac{9}{4} \) is close to \( \sqrt{5} \).
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