To solve the expression \( 7\sqrt{5} - 2\sqrt{5} \):

1. Both terms have a common factor of \( \sqrt{5} \).
2. You can factor out \( \sqrt{5} \) from both terms:

\[
7\sqrt{5} - 2\sqrt{5} = (7 - 2)\sqrt{5}
\]

3. Simplify the expression inside the parentheses:

\[
(7 - 2)\sqrt{5} = 5\sqrt{5}
\]

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

Would you like more details or have any questions about this? Here are five related questions to expand on this topic:

1. How do you add or subtract like radicals?
2. What are the rules for simplifying expressions involving square roots?
3. How would you simplify \( 3\sqrt{2} + 4\sqrt{2} \)?
4. What happens if the square roots have different radicands?
5. How would you multiply two radical expressions like \( \sqrt{3} \times \sqrt{12} \)?

**Tip:** Always look for common factors when simplifying radical expressions to combine like terms easily.

Learn how to simplify the expression 7√5 - 2√5 step-by-step with a detailed explanation. This problem involves algebraic manipulation of radical expressions and is suitable for high school students.

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