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Step 1:I'll solve this step by step using the guidelines you specified:
Step 2:: Simplify inside the square root
- $$18 = 2 \cdot 3^{2}
- First, break down 18 into its prime factors
Step 3:: Rewrite the square root using prime factorization
- $$\sqrt{18} = \sqrt{2 \cdot 3^{2}}
- = \sqrt{2} \cdot \sqrt{3^{2}}
Step 4:: Simplify the square root of 3^{2}
- $$\sqrt{3^{2}} = 3
Step 5:: Rewrite the original expression
- $$2\sqrt{18} = 2 \cdot \sqrt{2} \cdot 3
Step 6:: Simplify
- $$2\sqrt{18} = 2 \cdot 3 \cdot \sqrt{2}
- = 6\sqrt{2}
Final Answer
6\sqrt{2}
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