Determine if square root of, 8, end square root 
8
​
  is rational or irrational and give a reason for your answer.

The square root of 8, denoted as \( \sqrt{8} \), is **irrational**.

### Reason:
A rational number can be expressed as a fraction \( \frac{a}{b} \), where both \( a \) and \( b \) are integers and \( b \neq 0 \). However, \( \sqrt{8} \) cannot be expressed as such a fraction. To see why:

- The exact value of \( \sqrt{8} \) is approximately 2.8284271... (an infinite non-repeating decimal).
- Since this decimal neither terminates nor repeats, \( \sqrt{8} \) does not fit the definition of a rational number.

Therefore, \( \sqrt{8} \) is **irrational**.

Do you want more details or have any questions?

### Related Questions:
1. What are the conditions for a number to be rational?
2. Can the square root of any whole number ever be rational?
3. How can we simplify \( \sqrt{8} \)?
4. What is the difference between rational and irrational numbers?
5. Are there any whole numbers whose square roots are rational?

#### Tip:
If the square root of a number is not a perfect square, it will always be irrational.

Determine if square root of 8 is rational or irrational and give a reason for your answer.

Determine whether the square root of 8 is rational or irrational. Explore number theory concepts, including irrational numbers and square roots. Learn why the square root of 8 cannot be expressed as a fraction, making it irrational. Suitable for students in Grades 7-10.

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