https://file.aiquickdraw.com/mathbot/file/1725380116132eb9d7bn4.jpg

The expression given in the image is:

\[
5\sqrt{30} \div 6\sqrt{5}
\]

### Simplifying the expression:
1. Rewrite the given expression as a fraction:
   \[
   \frac{5\sqrt{30}}{6\sqrt{5}}
   \]

2. Simplify the square roots. We can express \(\sqrt{30}\) as:
   \[
   \sqrt{30} = \sqrt{5 \times 6} = \sqrt{5} \times \sqrt{6}
   \]

   Now substitute this into the expression:
   \[
   \frac{5\sqrt{5}\sqrt{6}}{6\sqrt{5}}
   \]

3. Cancel out \(\sqrt{5}\) from both the numerator and denominator:
   \[
   \frac{5\sqrt{6}}{6}
   \]

4. The final simplified expression is:
   \[
   \frac{5\sqrt{6}}{6}
   \]

This is the simplest form of the given expression.

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. How do you simplify square root expressions with multiplication?
2. Can all square root expressions be simplified further?
3. How do you handle division with square roots and integers?
4. What are common properties of square roots that make simplification easier?
5. How would you simplify a more complex expression involving multiple square roots?

**Tip:** When simplifying expressions with square roots, try to factor numbers under the square root into prime factors to find common terms.

Explore the step-by-step solution to simplify the radical expression 5√30 ÷ 6√5. This problem covers concepts such as simplifying square roots and division of radicals, suitable for students in Grades 9-10.

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