To simplify the given expression:

$\sqrt{6(\sqrt{2} + 3)}$

We will work step by step:

Step 1: Distribute inside the square root

Using the distributive property, expand $6(\sqrt{2} + 3)$:

$6(\sqrt{2} + 3) = 6\sqrt{2} + 18$

So the expression becomes:

$\sqrt{6\sqrt{2} + 18}$

Step 2: Factor out a common factor (if possible)

Notice that $18$ and $6\sqrt{2}$ do not simplify further since they don’t have common radicals. Thus, the simplified form remains:

$\sqrt{6\sqrt{2} + 18}$

This is as simplified as possible unless further clarification is given about breaking it into prime factors or further factoring.

Would you like further clarification, or do you have any specific conditions for further simplification? Let me know!

Questions for You:

1. Do you want to rewrite the expression as a decimal approximation instead?
2. Should I simplify further under additional constraints?
3. Are you looking to expand this into a polynomial expression?
4. Is there a specific technique you'd like me to explore for radical simplification?
5. Would you like to see examples of similar problems?

Tip:

When simplifying square roots, always look for common factors that can be factored out to reduce the expression.