Let's simplify the given expression:

$\sqrt{27} + \sqrt{12} - \sqrt{48}$

Step 1: Simplify each square root term.

• $\sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \times \sqrt{3} = 3\sqrt{3}$
• $\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}$
• $\sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3}$

Step 2: Substitute the simplified forms into the expression:

$3\sqrt{3} + 2\sqrt{3} - 4\sqrt{3}$

Step 3: Combine like terms:

$(3 + 2 - 4)\sqrt{3} = 1\sqrt{3} = \sqrt{3}$

So, the simplified value of the expression is:

$\boxed{\sqrt{3}}$

Would you like more details, or do you have any questions?

Here are 5 related questions:

1. How do you simplify a square root when the number inside is not a perfect square?
2. Can all square roots be simplified into radical form like in this problem?
3. What is the general method for combining like terms with square roots?
4. How do you simplify more complex expressions with multiple square roots?
5. What is the decimal approximation of $\sqrt{3}$?

Tip: Always try to factor out perfect squares when simplifying square roots!