Question

9/4 is close to the square root of what integer? (1 point)


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Answer 1

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:

\[
\boxed{5}
\]