Simplify 300−−−√.(1 point) Responses 512−−√ 5 start root 12 end root 1003–√ 100 start root 3 end root This radical expression is already fully simplified. This radical expression is already fully simplified. 103–√

To simplify the expression \( \sqrt{300} \), we start by factoring 300 into its prime factors.

1. Factor 300:
\[
300 = 3 \times 100 = 3 \times 10^2 = 3 \times (2 \times 5)^2 = 3 \times 2^2 \times 5^2
\]

2. Now we can apply the square root:
\[
\sqrt{300} = \sqrt{3 \times 100} = \sqrt{3 \times 10^2}
\]

3. Since \( \sqrt{10^2} = 10 \):
\[
\sqrt{300} = \sqrt{3} \times 10 = 10 \sqrt{3}
\]

Thus, \( \sqrt{300} \) simplifies to \( 10 \sqrt{3} \).

Now let's consider the response options you provided:

- \( 512^{-\frac{1}{2}} \)
- \( \sqrt{12} \)
- \( 100\sqrt{3} \)
- This radical expression is already fully simplified.
- \( \sqrt{103} \)

The simplified form we found, \( 10 \sqrt{3} \), is not among the response options. However, the correct answer regarding the simplification of \( \sqrt{300} \) is indeed \( 10 \sqrt{3} \).

For the purpose of your question, it's important to note that \( \sqrt{300} \) can be confirmed as \( 10 \sqrt{3} \), which is already in its simplest form.