$$ {\displaylines\\ does\,\sqrt{5+\sqrt{6=\sqrt{11}}}} $$

The expression you've written seems to have a typo and is not fully clear. I'll correct it based on what I think you're trying to ask.

You likely intended to ask whether the following expression holds true:

\[
\sqrt{5 + \sqrt{6}} = \sqrt{11}
\]

Let's check if this is true by squaring both sides of the equation:

1. **Start with the equation**:
   \[
   \sqrt{5 + \sqrt{6}} = \sqrt{11}
   \]

2. **Square both sides** to remove the square roots:
   \[
   5 + \sqrt{6} = 11
   \]

3. **Subtract 5 from both sides**:
   \[
   \sqrt{6} = 6
   \]

This implies that the square root of 6 equals 6, which is false because $\sqrt{6}$ is approximately 2.449, not 6.

Therefore, the original equation $\sqrt{5 + \sqrt{6}} = \sqrt{11}$ does not hold true.

Would you like more details or have any other questions?

Here are 5 related questions:
1. What is the value of $\sqrt{11}$?
2. How do you approximate square roots of non-perfect squares?
3. Can you simplify the expression $\sqrt{5 + \sqrt{6}}$ further?
4. How do you solve equations involving nested square roots?
5. What are some common properties of square roots?

**Tip:** When comparing two square roots, squaring both sides can help determine if they are equal.

Explore the equation √(5 + √6) = √11 and learn how to verify its correctness step-by-step. This problem involves square roots and their properties, suitable for high school students.

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