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Step 1:I'll solve this step-by-step using the specified LaTeX formatting guidelines:
Step 2:: Identify the number under the square root
The problem is to simplify $$\sqrt{324}
Step 3:: Find the largest perfect square factor
To simplify a square root, we want to find the largest perfect square that divides 324 evenly.
Step 4:: Prime factorization of 324
324 = 2^{2} \times 3^{4}
Step 5:: Group perfect square factors
We can see that $$2^{2}$$ and $$3^{4}$$ can be taken out of the square root:
\sqrt{324} = \sqrt{2^{2} \times 3^{4}} = \sqrt{(2^{2} \times 3^{4})}
Step 6:: Simplify the square root
\sqrt{324} = 2^{1} \times 3^{2} = 2 \times 9 = 18
Final Answer
\sqrt{324} = 18
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