Question

which of the following are irrational numbers 8/5 pi -2 -10

Answer 1

To determine which of the numbers in the list are irrational, let's analyze each one:

1. **8/5**: This is a rational number because it can be expressed as a fraction of two integers (8 and 5).

2. **π (pi)**: This is an irrational number. It cannot be expressed as a fraction of two integers.

3. **-2**: This is a rational number because it can be expressed as -2/1.

4. **-10**: This is also a rational number because it can be expressed as -10/1.

Now, let's consider the expression \( \frac{8}{5} \pi - 2 \):

- Since \( \pi \) is irrational, any non-zero rational number multiplied by \( \pi \) (like \( \frac{8}{5} \)) will also be irrational.
- Moreover, subtracting a rational number (like -2) from an irrational number (like \( \frac{8}{5} \pi \)) will still yield an irrational number.

Therefore, the only irrational number from the list is:

- \( \frac{8}{5} \pi - 2 \)

So, the answer is **\( \frac{8}{5} \pi - 2 \)** is the only irrational number in the list.