Question

algebra: concepts and connections - plc investigating rational and irrational numbers simplify \\(\sqrt{18}\\). options: \\(6\sqrt{2}\\), \\(2\sqrt{6}\\), \\(3\sqrt{2}\\), (another option with \\(\sqrt{2}\\) maybe)

Explanation:

Step1: Factor 18 into perfect square

$\sqrt{18} = \sqrt{9 \times 2}$

Step2: Split square root of product

$\sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2}$

Step3: Simplify $\sqrt{9}$

$\sqrt{9} = 3$, so $3 \times \sqrt{2} = 3\sqrt{2}$

Answer:

$3\sqrt{2}$