Let's solve the given expression:

$5\sqrt{3} + \sqrt{12}$

Step 1: Simplify $\sqrt{12}$

We know that:

$\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}$

Step 2: Substitute back into the expression

Now, we substitute $\sqrt{12}$ with $2\sqrt{3}$:

$5\sqrt{3} + 2\sqrt{3}$

Step 3: Combine like terms

Since both terms have $\sqrt{3}$, we can combine them:

$(5 + 2)\sqrt{3} = 7\sqrt{3}$

Final Answer

The simplified form of the expression is:

$7\sqrt{3}$

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Do you have any further questions or would you like additional details?

Here are some related questions you might find helpful:

1. How do you simplify square roots of larger numbers?
2. What are the general rules for combining like radical terms?
3. How can you break down square roots with more complex factors?
4. What happens if the radicals contain different numbers? How would you simplify them then?
5. How can you express a radical in simplest form?

Tip: Always look for perfect square factors within the square root to simplify the expression easily!