Question

check all statements that are true.
since 3 is not a perfect square, $sqrt{3}$ is rational.
since it is a ratio of two integers, $\frac{3}{7}$ is rational.
since 25 is a perfect square, $sqrt{25}$ is irrational.
since it is an integer, $-1$ is rational.
since it is a repeating decimal, $19.overline{58}$ is irrational.
none of the above statements are true.

Explanation:

Step1: Analyze first statement

Non-perfect square roots are irrational, so $\sqrt{3}$ is irrational. Statement 1 is false.

Step2: Analyze second statement

A rational number is a ratio of integers ($3$ and $7$). Statement 2 is true.

Step3: Analyze third statement

$\sqrt{25}=5$, an integer (rational). Statement 3 is false.

Step4: Analyze fourth statement

Integers are rational (e.g., $-1=\frac{-1}{1}$). Statement 4 is true.

Step5: Analyze fifth statement

Repeating decimals are rational. Statement 5 is false.

Step6: Analyze sixth statement

Some statements are true, so this is false.

Answer:

Since it is a ratio of two integers, $\frac{3}{7}$ is rational., Since it is an integer, $-1$ is rational.