Problem 122 - Algebra and Trigonometry

Question

Explain how to add \(\sqrt{3}+\sqrt{12}\)

Step-by-Step Solution

Answer

The result of \( \sqrt{3} + \sqrt{12} \) is \(3\sqrt{3}\)

Step 1: Simplify the Square Root

To simplify \(\sqrt{12}\), find a factor of 12 that is a perfect square. The largest perfect square factor of 12 is 4. So, break down \(\sqrt{12}\) to: \(\sqrt{4} * \sqrt{3} = 2\sqrt{3}\).

Step 2: Add the Square Roots

Now, add \(\sqrt{3}\) and \(2\sqrt{3}\) together. Since they have the same radical part, we can add them directly to get: \(3\sqrt{3}\)