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The problem asks to choose the correct names for the set of numbers provided: 

\[
\left\{ \sqrt{17}, -15.62\ldots, 2\pi, -\sqrt{8} \right\}
\]

Let's analyze these numbers:

1. **\(\sqrt{17}\)**: This is the square root of a non-perfect square, so it is an irrational number.
2. **\(-15.62\ldots\)**: This appears to be a non-repeating, non-terminating decimal, which is also an irrational number.
3. **\(2\pi\)**: Since \(\pi\) is irrational, \(2\pi\) is also irrational.
4. **\(-\sqrt{8}\)**: This is another square root of a non-perfect square, hence irrational.

Given this information, the correct name for the set of numbers is **irrational numbers**.

Would you like more details, or do you have any questions? 

Here are 5 related questions you might find interesting:
1. What are the differences between rational and irrational numbers?
2. How can we determine if a number is irrational?
3. Are all square roots irrational?
4. Why is \(\pi\) considered an irrational number?
5. Can irrational numbers be expressed as a fraction?

**Tip:** Remember, irrational numbers cannot be expressed as exact fractions, and their decimal representation neither terminates nor repeats.

Choose the correct names for the set of numbers: {√17, -15.62…, 2π, -√8}

Determine the correct classification of a set of numbers including √17, -15.62…, 2π, and -√8. Learn about irrational numbers, their properties, and how to identify them.

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