To simplify \( \sqrt{300} \), we first break 300 into its prime factors.

\[
300 = 2^1 \times 3^1 \times 5^2
\]

We then use the property of square roots: 

\[
\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}
\]

So,

\[
\sqrt{300} = \sqrt{2 \times 3 \times 5^2}
\]

Now, simplify by taking the square root of perfect squares:

\[
\sqrt{300} = \sqrt{2} \times \sqrt{3} \times \sqrt{5^2}
\]

\[
\sqrt{300} = \sqrt{2} \times \sqrt{3} \times 5
\]

Thus, the simplified form is:

\[
\sqrt{300} = 5\sqrt{6}
\]

### Final Answer:
\[
\sqrt{300} = 5\sqrt{6}
\]

Would you like further details on this? Here are some related questions:

1. How do you simplify larger radicals?
2. What are the prime factorization techniques?
3. How can you simplify radicals with variables?
4. What are the properties of square roots?
5. How do you rationalize denominators

Learn how to simplify the radical \( \sqrt{300} \) using prime factorization and the properties of square roots. This problem covers the step-by-step simplification process, breaking down 300 into prime factors, and taking square roots of perfect squares. Suitable for students in Grades 9-11.

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