https://file.aiquickdraw.com/mathbot/file/1726128103735wmnbo8st.jpg

The expression from the image is:

\[
5 \cdot \sqrt{5} + \frac{1}{2} \cdot \sqrt{20} - \frac{5}{4} \cdot \sqrt{50}
\]

Let's break it down and simplify each term:

1. \( \sqrt{5} \) is already in its simplest form.
2. \( \sqrt{20} = \sqrt{4 \cdot 5} = 2\sqrt{5} \), so \( \frac{1}{2} \cdot \sqrt{20} = \frac{1}{2} \cdot 2\sqrt{5} = \sqrt{5} \).
3. \( \sqrt{50} = \sqrt{25 \cdot 2} = 5\sqrt{2} \), so \( \frac{5}{4} \cdot \sqrt{50} = \frac{5}{4} \cdot 5\sqrt{2} = \frac{25}{4}\sqrt{2} \).

Thus, the expression becomes:

\[
5\sqrt{5} + \sqrt{5} - \frac{25}{4} \cdot \sqrt{2}
\]

Now, let's simplify:

\[
(5 + 1)\sqrt{5} - \frac{25}{4} \cdot \sqrt{2} = 6\sqrt{5} - \frac{25}{4} \cdot \sqrt{2}
\]

This is the simplified form of the expression.

Would you like further details or explanations? Here are 5 related questions you might find useful:

1. How do you simplify square roots with different radicands?
2. How can rational coefficients affect the simplification process?
3. What methods can be used to approximate square roots for numerical calculations?
4. How does factoring numbers help in simplifying square roots?
5. What are some common mistakes to avoid when simplifying square root expressions?

**Tip:** Always break down square roots into their prime factors to simplify them efficiently.

Solve the expression 5 * sqrt(5) + (1/2) * sqrt(20) - (5/4) * sqrt(50).

Discover how to simplify the radical expression 5 * sqrt(5) + (1/2) * sqrt(20) - (5/4) * sqrt(50) step by step. Learn about properties of square roots and breaking down radicals in this algebra problem, suitable for students in Grades 9-11.

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