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QuestionMathematics

Simplify √324
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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