Question

check all statements that are true:

• since it is a ratio of two integers, \\(\frac{9}{15}\\) is rational.
• since it is a terminating decimal, 2.9 is irrational.
• since 11 is not a perfect square, \\(sqrt{11}\\) is rational.
• since 49 is a perfect square, \\(sqrt{49}\\) is rational.
• since it is an integer, 2 is irrational.
• none of the above statements are true.

Explanation:

• A rational number is a ratio of two integers (denominator non-zero). $\frac{9}{13}$ fits this definition, so the first statement is true.
• Terminating decimals are rational, so 2.9 being irrational is false.
• Non-perfect square roots are irrational, so $\sqrt{11}$ rational is false.
• $\sqrt{49}=7$, an integer (rational), so the fourth statement is true.
• Integers are rational, so 2 being irrational is false.
• The first and fourth statements are true, so "none" is false.

Answer:

Since it is a ratio of two integers, $\frac{9}{13}$ is rational; Since 49 is a perfect square, $\sqrt{49}$ is rational.