Question

check all statements that are true:

• since 36 is a perfect square, $sqrt{36}$ is rational.
• since it is a repeating decimal, $12.overline{8}$ is irrational.
• since 7 is not a perfect square, $sqrt{7}$ is irrational.
• since it is a ratio of two integers, $\frac{5}{12}$ is irrational.
• since it is a terminating decimal, 5.29 is rational.
• none of the above statements are true.

Explanation:

• $\sqrt{36}=6$, a rational number (perfect square roots are rational).
• $12.\overline{8}$ is repeating, so rational (repeating decimals are rational, so the statement is false).
• $\sqrt{7}$ is non-perfect square root, irrational (true).
• $\frac{5}{12}$ is ratio of integers, rational (statement is false).
• 5.29 terminates, so rational (true).
• The first, third, and fifth statements are true.

Answer:

Since 36 is a perfect square, $\sqrt{36}$ is rational; Since 7 is not a perfect square, $\sqrt{7}$ is irrational; Since it is a terminating decimal, 5.29 is rational.