To simplify \(\sqrt{180}\), we start by factoring 180 into its prime factors.
First, we can break down 180 as follows:
\[ 180 = 18 \times 10 \] Next, we can factor 18 and 10:
\[ 18 = 9 \times 2 = 3^2 \times 2 \] \[ 10 = 5 \times 2 \]
Putting it all together, we have:
\[ 180 = 3^2 \times 2 \times 5 \times 2 = 3^2 \times 2^2 \times 5 \]
Now, we rewrite \(180\) using its prime factors:
\[ 180 = 2^2 \times 3^2 \times 5 \]
Next, we apply the property of square roots:
\[ \sqrt{180} = \sqrt{2^2 \times 3^2 \times 5} \]
We can take the square roots of the perfect squares:
\[ \sqrt{180} = \sqrt{2^2} \times \sqrt{3^2} \times \sqrt{5} = 2 \times 3 \times \sqrt{5} \]
This simplifies to:
\[ \sqrt{180} = 6\sqrt{5} \]
Thus, the simplified form of \(\sqrt{180}\) is:
\[ \boxed{6\sqrt{5}} \]