To solve the expression \( 3\sqrt{5} - \frac{10}{\sqrt{5}} \), we can simplify it as follows:

1. The expression is \( 3\sqrt{5} - \frac{10}{\sqrt{5}} \).
2. Simplify the second term by rationalizing the denominator:
   \[
   \frac{10}{\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}} = \frac{10\sqrt{5}}{5} = 2\sqrt{5}
   \]
3. Now, the expression becomes:
   \[
   3\sqrt{5} - 2\sqrt{5}
   \]
4. Subtract the like terms:
   \[
   (3 - 2)\sqrt{5} = 1\sqrt{5} = \sqrt{5}
   \]

So, the simplified result is \( \sqrt{5} \).

Would you like any more details on the solution or have any other questions?

Here are 5 related questions you might find interesting:
1. How do you rationalize the denominator in a fraction with a square root?
2. What are like terms, and how do you combine them?
3. How do you simplify expressions involving square roots?
4. What is the process of factoring square roots?
5. Can you apply this simplification method to higher-order roots?

**Tip:** When simplifying expressions involving square roots, always look for like terms to combine, and remember that rationalizing the denominator can help simplify fractions with square roots.

Learn how to simplify the expression 3√5 - 10/√5 step-by-step with a detailed solution. This problem involves square roots and rationalizing denominators to simplify the expression effectively. Suitable for high school students in Grades 9-12.

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