b. \( \sqrt{48}-\sqrt{12}+\sqrt{27} \)
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The Deep Dive
Did you know that simplifying square roots can make expressions much more manageable? For example, \(\sqrt{48}\) can be rewritten as \(\sqrt{16 \times 3} = 4\sqrt{3}\), \(\sqrt{12}\) as \(\sqrt{4 \times 3} = 2\sqrt{3}\), and \(\sqrt{27}\) as \(\sqrt{9 \times 3} = 3\sqrt{3}\). So, your expression becomes \(4\sqrt{3} - 2\sqrt{3} + 3\sqrt{3}\), which simplifies further to \(5\sqrt{3}\). Now imagine you're trying to impress a friend with your math skills at a gathering. Instead of presenting numbers in their clunky radical forms, you can confidently show off your simplified expression, \(5\sqrt{3}\). Your friends will be amazed by your ability to simplify complex expressions, and you might even inspire them to learn more about the beauty of mathematics right then and there!