Question

9 over 4 is close to the square root of what integer?

Answer 1

To find the integer that \( \frac{9}{4} \) is close to the square root of, we first calculate \( \frac{9}{4} \):

\[
\frac{9}{4} = 2.25
\]

Next, we need to determine the integer \( n \) such that \( \sqrt{n} \) is approximately equal to \( 2.25 \). To do this, we will square \( 2.25 \):

\[
(2.25)^2 = 5.0625
\]

This value, \( 5.0625 \), suggests that the integer we are looking for is approximately \( 5 \).

To confirm, we can check the square roots of integers around \( 5 \):

\[
\sqrt{5} \approx 2.236 \quad \text{and} \quad \sqrt{6} \approx 2.449
\]

Since \( 2.25 \) is between \( \sqrt{5} \) and \( \sqrt{6} \), we conclude that \( \frac{9}{4} \) is closest to the square root of \( 5 \).

Thus, \( \frac{9}{4} \) is close to the square root of the integer \( \boxed{5} \).