9. Simplify $\sqrt{2}+\sqrt{18}$
Final Answer: The simplified form of \(\sqrt{2}+\sqrt{18}\) is \(\boxed{4\sqrt{2}}\).
Step 1 :The problem is asking to simplify the expression \(\sqrt{2}+\sqrt{18}\).
Step 2 :First, we need to simplify \(\sqrt{18}\). We know that 18 equals 2 times 9, so \(\sqrt{18} = \sqrt{2 \times 9} = \sqrt{2} \times \sqrt{9} = \sqrt{2} \times 3\).
Step 3 :So, the expression becomes \(\sqrt{2} + \sqrt{2} \times 3 = \sqrt{2} + 3\sqrt{2}\).
Step 4 :The expression \(\sqrt{2} + 3\sqrt{2}\) can be simplified further to \(4\sqrt{2}\).
Step 5 :Final Answer: The simplified form of \(\sqrt{2}+\sqrt{18}\) is \(\boxed{4\sqrt{2}}\).