Find the square root of 324.

Answer

To find the square root of 324, we can follow these steps:

### Step 1: Factor the number 324
We start by finding the prime factors of 324. We can divide 324 by the smallest prime number, which is 2.

324 ÷ 2 = 162
162 ÷ 2 = 81

Now, we can no longer divide by 2, so we move to the next prime number, which is 3.

81 ÷ 3 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1

So, the prime factorization of 324 is:
\[ 324 = 2^2 \times 3^4 \]

### Step 2: Apply the square root property
Using the property of square roots, we can express the square root of a product of prime factors as follows:
\[ \sqrt{324} = \sqrt{2^2 \times 3^4} \]

### Step 3: Simplify the square root
We can separate the square root of each factor:
\[ \sqrt{324} = \sqrt{2^2} \times \sqrt{3^4} \]

Now, we can simplify each square root:
\[ \sqrt{2^2} = 2 \]
\[ \sqrt{3^4} = 3^2 = 9 \]

### Step 4: Multiply the results
Now we multiply the results from the previous step:
\[ \sqrt{324} = 2 \times 9 = 18 \]

### Final Answer
Thus, the square root of 324 is:
\[ \sqrt{324} = 18 \]

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