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The problem you provided involves a right triangle with angles of 30° and 60°, and we are asked to find the length of side \(x\) in simplest radical form with a rational denominator.

We can apply the following steps:

### Step 1: Identify the triangle type
This is a 30°-60°-90° right triangle, which has a known side ratio for the sides opposite these angles: 
- The side opposite the 30° angle is \( \frac{1}{2} \) the hypotenuse.
- The side opposite the 60° angle is \( \frac{\sqrt{3}}{2} \) the hypotenuse.

### Step 2: Assign triangle sides based on the given values
- The hypotenuse is given as \( \sqrt{8} \).
- We need to find the side \( x \), which is opposite the 30° angle.

### Step 3: Use the ratio for a 30°-60°-90° triangle
In this type of triangle:
- The side opposite the 30° angle is half of the hypotenuse.
  
So, 
\[
x = \frac{1}{2} \times \sqrt{8} = \frac{\sqrt{8}}{2}
\]

### Step 4: Simplify the radical
\[
\sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}
\]
Now substitute this into the equation for \(x\):
\[
x = \frac{2\sqrt{2}}{2} = \sqrt{2}
\]

Thus, the length of side \( x \) is \( \sqrt{2} \).

### Final Answer:
\[
x = \sqrt{2}
\]

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

Here are 5 related questions:
1. How do you calculate the hypotenuse in a 30°-60°-90° triangle?
2. What are the properties of 30°-60°-90° triangles?
3. How can you rationalize a denominator if a radical is present in a fraction?
4. What are the other trigonometric ratios for a 30°-60°-90° triangle?
5. How would the solution change if the hypotenuse was a different value?

**Tip:** Always check if a radical can be simplified by factoring out perfect squares, which helps in getting the simplest form.

Find the length of side x in simplest radical form with a rational denominator in a right triangle with angles 30°, 60°, and hypotenuse √8.

This guide demonstrates how to find the length of side x in a 30°-60°-90° triangle using simple radical form with a rational denominator. The hypotenuse is √8, and we apply trigonometric properties for accurate calculation. Suitable for students in Grades 8-10.

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