Case context: A calculator shows $\sqrt{9}=3$ and $\sqrt{5}\approx2.24$.

Question: Classify each calculator result as exact or approximate. Then explain why the second result is approximate.

Sample answer: $\sqrt{9}=3$ is exact because $9$ is a perfect square. $\sqrt{5}\approx2.24$ is approximate because $5$ is not a perfect square and the calculator displays a limited, rounded number of digits. Also, $(2.24)^2=5.0176$, not exactly $5$.

Key points:

• $\sqrt{9}=3$ is exact.
• $9$ is a perfect square.
• $\sqrt{5}\approx2.24$ is approximate.
• $5$ is not a perfect square.
• The displayed decimal is limited or rounded, and its square is not exactly $5$.

Rubric: The answer must classify both results correctly and give two valid reasons why 2.24 is an approximation of $\sqrt{5}$.