To simplify \( \sqrt{300} \), we can start by factoring 300 into its prime factors:
\[ 300 = 3 \times 100 = 3 \times 10^2 = 3 \times (2 \times 5)^2 = 3 \times 2^2 \times 5^2 \]
We can rewrite \( 300 \) as:
\[ 300 = 3 \times 2^2 \times 5^2 \]
Now, we take the square root:
\[ \sqrt{300} = \sqrt{3 \times 2^2 \times 5^2} \]
Using the property of square roots (\( \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} \)), we get:
\[ \sqrt{300} = \sqrt{3} \times \sqrt{2^2} \times \sqrt{5^2} = \sqrt{3} \times 2 \times 5 \]
Thus, simplifying further:
\[ \sqrt{300} = 10\sqrt{3} \]
Therefore, the simplified form of \( \sqrt{300} \) is:
\[ \boxed{10\sqrt{3}} \]
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