To simplify \( 3 \) radical over \( 8 \), which can be written as \( \frac{3}{\sqrt{8}} \):

1. First, simplify the square root of \( 8 \). We know:
   \[
   \sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}
   \]

2. Substitute this into the expression:
   \[
   \frac{3}{\sqrt{8}} = \frac{3}{2\sqrt{2}}
   \]

3. To rationalize the denominator, multiply both the numerator and the denominator by \( \sqrt{2} \):
   \[
   \frac{3}{2\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{3\sqrt{2}}{2 \times 2} = \frac{3\sqrt{2}}{4}
   \]

So, the simplified form of \( \frac{3}{\sqrt{8}} \) is \( \frac{3\sqrt{2}}{4} \).

Would you like further details or have any questions?

Here are five related questions:

1. How do you simplify \(\frac{5}{\sqrt{12}}\)?
2. What is the simplified form of \(\frac{7}{\sqrt{18}}\)?
3. How do you rationalize the denominator of \(\frac{4}{\sqrt{10}}\)?
4. Can you simplify \(\frac{2}{\sqrt{5}}\)?
5. What is the square root of a fraction, such as \(\sqrt{\frac{9}{16}}\)?

**Tip:** When simplifying expressions involving square roots, always look for ways to rationalize the denominator, which means eliminating the square root from the denominator.

Learn how to simplify 3 radical over 8 step-by-step with detailed explanations. This problem involves square roots and rationalizing denominators. Suitable for students in Grades 7-9.

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