To determine which integer’s square root is close to [tex]\(\frac{9}{4}\)[/tex], we can proceed with the following steps:
1. First, express [tex]\(\frac{9}{4}\)[/tex] in decimal form for easier handling. The fraction [tex]\(\frac{9}{4}\)[/tex] is equal to 2.25.
2. We're seeking an integer whose square root is approximated by 2.25. To find this integer, we consider the relationship and square both sides:
[tex]\[ x \approx (2.25)^2 \][/tex]
3. We calculate the square of 2.25:
[tex]\[
2.25^2 = 2.25 \times 2.25 = 5.0625
\][/tex]
4. Therefore, 5.0625 is very close to 5, making 5 the nearest integer to [tex]\(2.25^2\)[/tex].
Thus, the integer whose square root is approximately [tex]\(\frac{9}{4}\)[/tex] or 2.25 is [tex]\(\boxed{5}\)[/tex].
