To simplify \(\left(\frac{11}{18}\right)^{1/2}\), follow these steps:

### Step-by-step solution:
1. **Recognize the exponent**: The expression \(\left(\frac{11}{18}\right)^{1/2}\) is the square root of \(\frac{11}{18}\), because raising something to the power of \(1/2\) is the same as taking its square root.

2. **Apply the square root to both the numerator and denominator**:
   \[
   \left(\frac{11}{18}\right)^{1/2} = \frac{\sqrt{11}}{\sqrt{18}}
   \]

3. **Simplify the denominator**: 
   \[
   \sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}
   \]
   So, the expression becomes:
   \[
   \frac{\sqrt{11}}{3\sqrt{2}}
   \]

4. **Rationalize the denominator**: To eliminate the square root in the denominator, multiply both the numerator and denominator by \(\sqrt{2}\):
   \[
   \frac{\sqrt{11}}{3\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{11} \times \sqrt{2}}{3 \times 2} = \frac{\sqrt{22}}{6}
   \]

### Final simplified form:
\[
\frac{\sqrt{22}}{6}
\]

This is the simplified form of \(\left(\frac{11}{18}\right)^{1/2}\).

Would you like more details or have any questions about this? 

Here are 5 related questions to further explore:
1. How do you simplify \(\left(\frac{7}{12}\right)^{1/2}\)?
2. What is the result of rationalizing \(\frac{1}{\sqrt{5}}\)?
3. How do you simplify \(\left( \frac{25}{36} \right)^{1/2}\)?
4. Can you explain the process of rationalizing a denominator?
5. How do you compute \(\left( \frac{5}{8} \right)^{1/3}\)?

**Tip**: When simplifying square roots with fractions, always try to rationalize the denominator if it contains a square root.

Learn how to simplify (11/18)^(1/2) with this detailed guide. This solution walks you through algebraic concepts like simplifying radicals, rationalizing the denominator, and handling fractions under square roots. Suitable for students in Grades 9-10.

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