Let's simplify and solve the expression step by step:

The expression is:

\[
3\sqrt{5} + \sqrt{20} - \sqrt{45} + \sqrt{5}
\]

1. **Simplify \(\sqrt{20}\):**

\[
\sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5}
\]

2. **Simplify \(\sqrt{45}\):**

\[
\sqrt{45} = \sqrt{9 \times 5} = 3\sqrt{5}
\]

Now, substitute the simplified values back into the expression:

\[
3\sqrt{5} + 2\sqrt{5} - 3\sqrt{5} + \sqrt{5}
\]

3. **Combine like terms (all terms contain \(\sqrt{5}\)):**

\[
(3 + 2 - 3 + 1)\sqrt{5} = 3\sqrt{5}
\]

So, the simplified expression is:

\[
3\sqrt{5}
\]

Would you like further details or have any questions about the steps?

Here are some related questions:
1. How do you simplify square roots involving multiplication?
2. Can you combine square roots with different radicands?
3. What are like terms, and how do you combine them in algebraic expressions?
4. How does factoring help in simplifying square roots?
5. What is the process for rationalizing square roots?

**Tip:** Always look for perfect square factors when simplifying square roots.

Learn how to simplify the expression 3√5 + √20 - √45 + √5 step-by-step. This problem involves simplifying square roots and combining like terms, perfect for students in Grades 7-9 learning about radicals and algebra.

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