Problem 122 - College Algebra

Question

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

Step-by-Step Solution

Answer

Therefore, \(\sqrt{3} + \sqrt{12} = 3\sqrt{3}\)

Step 1: Simplify the Square Roots

Firstly, simplify \( \sqrt{12} \) as it can be reduced to a more simple form. The number 12 can be expressed as the product of 4 and 3 where 4 is a perfect square. Therefore, \( \sqrt{12} \) can be expressed as: \[ \sqrt{12} = \sqrt{4 x 3} \] Then, we distribute the square root as follows:\[ \sqrt{12} = \sqrt{4} x \sqrt{3} = 2\sqrt{3} \]

Step 2: Perform the Addition

After the simplification, the equation becomes: \[ \sqrt{3} + 2\sqrt{3} \] Which can be interpreted as the addition of like terms, similary to \(1x + 2x = 3x\). So basically, this translates to: \[ 1\sqrt{3} + 2\sqrt{3} = 3\sqrt{3} \]