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From the image you shared, the answers provided are as follows:

1. For \( \sqrt{6} \), the selected answer is "Irrational".
2. For \( \sqrt[3]{8} \), the selected answer is also "Irrational".

Let's verify:

1. **\( \sqrt{6} \)**: The square root of 6 cannot be expressed as a ratio of two integers, so it is indeed an **irrational number**.

2. **\( \sqrt[3]{8} \)**: The cube root of 8 is equal to 2, because \( 2^3 = 8 \). Since 2 is a whole number, it is a **rational number**, not irrational**.

So, the second answer should be corrected to "Rational".

Would you like more details or further clarification?

Here are 5 related questions for further exploration:
1. What is the difference between rational and irrational numbers?
2. Can all cube roots of perfect cubes be considered rational?
3. Why is \( \sqrt{2} \) irrational while some square roots are rational?
4. Are there any other square roots of whole numbers that are rational?
5. How can we prove that a number is irrational?

**Tip:** Always check if a root simplifies to a whole number to determine its rationality.

The user provided a question related to determining whether the square root of 6 and the cube root of 8 are rational or irrational.

Explore the rationality of √6 and ∛8 with detailed explanations. Understand why √6 is irrational and why ∛8 is rational, using properties of roots and rational numbers. Ideal for students in Grades 7-10.

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