To simplify the expression $\sqrt{27} - \sqrt{12}$, let's break each square root down:

1. Simplify $\sqrt{27}$: $\sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \times \sqrt{3} = 3\sqrt{3}$

2. Simplify $\sqrt{12}$: $\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}$

Now, substitute these simplified values into the expression: $\sqrt{27} - \sqrt{12} = 3\sqrt{3} - 2\sqrt{3}$

Since both terms have $\sqrt{3}$, you can combine them: $(3 - 2)\sqrt{3} = 1\sqrt{3} = \sqrt{3}$

Thus, the simplified result is: $\sqrt{3}$

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Would you like a more detailed explanation or have any follow-up questions? Here are some related questions:

1. How can you simplify square roots of products like $\sqrt{45}$?
2. What is the general rule for simplifying square roots of perfect squares?
3. Can this method be used for higher-order roots like cube roots or fourth roots?
4. How do you rationalize a denominator involving square roots, such as $\frac{1}{\sqrt{2}}$?
5. What are some other common square root simplifications to know?

Tip: When simplifying square roots, always look for perfect square factors (like 4, 9, 16, etc.) that can be pulled out of the root.