To simplify \(\sqrt{600}\), we start by factorizing 600:
\[ 600 = 100 \times 6 = 10^2 \times 6 \]
Now we can express \(\sqrt{600}\) as:
\[ \sqrt{600} = \sqrt{10^2 \times 6} = 10 \sqrt{6} \]
Next, we want to find an expression equivalent to \(\sqrt{600}\).
Looking at the answer choices:
a. \(\frac{6}{\sqrt{10}}\)
b. \(\frac{10}{\sqrt{6}}\)
c. \(\frac{24}{\sqrt{25}}\)
d. \(\frac{25}{\sqrt{24}}\)
Let's analyze option b:
\[ \frac{10}{\sqrt{6}} \times \frac{\sqrt{6}}{\sqrt{6}} = \frac{10\sqrt{6}}{6} = \frac{5\sqrt{6}}{3} \]
This does not simplify to our equivalent expression.
Now, we can check option a:
\[ \frac{6}{\sqrt{10}} \times \frac{\sqrt{10}}{\sqrt{10}} = \frac{6\sqrt{10}}{10} = \frac{3\sqrt{10}}{5} \]
This also does not simplify correctly.
For option c:
\[ \frac{24}{\sqrt{25}} = \frac{24}{5} \]
And for option d:
\[ \frac{25}{\sqrt{24}} \quad (\text{which does not relate to } \sqrt{600}) \]
None of these seem to directly lead to \(\sqrt{600} = 10\sqrt{6}\).
Thus, after evaluating all options, it's clear option b, \(\frac{10}{\sqrt{6}}\), seems the closest as:
\[ \frac{10}{\sqrt{6}} = 10 \cdot \frac{\sqrt{6}}{6} = \frac{10\sqrt{6}}{6} \]
Hence the answer is:
\(\boxed{\frac{10}{\sqrt{6}}}\) (Option b)