https://file.aiquickdraw.com/mathbot/file/1725582704436w7fu0qlg.jpg

The image shows the following mathematical expression:

\[
\frac{5\sqrt{125}}{3\sqrt{2}}
\]

Let's simplify this expression step by step:

1. Start by simplifying the square roots:
   \[
   \sqrt{125} = \sqrt{25 \times 5} = 5\sqrt{5}
   \]
   
2. Now substitute this into the expression:
   \[
   \frac{5 \times 5\sqrt{5}}{3\sqrt{2}} = \frac{25\sqrt{5}}{3\sqrt{2}}
   \]

3. You can rationalize the denominator by multiplying both the numerator and denominator by \(\sqrt{2}\):
   \[
   \frac{25\sqrt{5}}{3\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{25\sqrt{10}}{3 \times 2} = \frac{25\sqrt{10}}{6}
   \]

So, the simplified expression is:

\[
\frac{25\sqrt{10}}{6}
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you simplify other square roots like \(\sqrt{50}\) or \(\sqrt{72}\)?
2. How do you rationalize the denominator in more complex expressions?
3. What happens when you add or subtract terms involving square roots?
4. Can this technique be used with cube roots or higher roots?
5. How would this process differ if the denominator were a complex number?

**Tip:** When simplifying square roots, always look for perfect squares within the number to make the process easier.

Simplify the radical expression 5√125 / 3√2 step by step, involving simplifying square roots and rationalizing the denominator. This problem highlights important techniques for simplifying radicals and expressions with square roots. Ideal for students in Grades 9-12.

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