Simplify the square root of 27.

1. Factor the radicand: The radicand is the number inside the square root, which is 27. We need to find the largest perfect square that divides 27. The factors of 27 are 1, 3, 9, and 27. The largest perfect square among these factors is 9.
$$ \sqrt{27} = \sqrt{9 \times 3} $$
2. Separate the square root: Using the property of square roots that $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$, we can separate the square root of the product into the product of the square roots.
$$ \sqrt{9 \times 3} = \sqrt{9} \times \sqrt{3} $$
3. Simplify the perfect square: The square root of 9 is 3, since $3^2 = 9$.
$$ \sqrt{9} = 3 $$
4. Combine the terms: Substitute the simplified square root back into the expression.
$$ 3 \times \sqrt{3} $$
This can be written more concisely as $3\sqrt{3}$.