Classify the numbers in the following list into categories like natural, integer, rational, and irrational. Then, identify one number from the list for each of the following categories: a) A natural n

Here are the numbers from the list: 5, $\sqrt{15}$, 23, $\sqrt{144}$, $-2$, 0.8.

Step 1: Classify each number.

• 5: Natural number, integer, rational number.
• $\sqrt{15}$: Irrational number (since 15 is not a perfect square).
• 23: Natural number, integer, rational number.
• $\sqrt{144}$: This simplifies to 12. So, 12 is a natural number, integer, rational number.
• $-2$: Integer, rational number (not a natural number).
• 0.8: Rational number (can be written as $\frac{8}{10}$ or $\frac{4}{5}$).

a) A natural number
Natural numbers are positive integers ($1, 2, 3, ...$). From the list, 5, 23, and $\sqrt{144}$ (which is 12) are natural numbers. We can pick any one.

The answer is $\boxed{5}$.

b) An irrational number
An irrational number cannot be expressed as a simple fraction and has a non-repeating, non-terminating decimal expansion. From the list, $\sqrt{15}$ is the only irrational number.

The answer is $\boxed{\sqrt{15}}$.