https://file.aiquickdraw.com/mathbot/file/1727218046933sib973jg.jpg

The expression shown in the image is:

\[
\sqrt{5} \left( \sqrt{10} + \sqrt{2} \right)
\]

We can simplify this by distributing \(\sqrt{5}\) over the terms inside the parentheses.

### Step 1: Distribute \(\sqrt{5}\)

\[
\sqrt{5} \left( \sqrt{10} + \sqrt{2} \right) = \sqrt{5} \times \sqrt{10} + \sqrt{5} \times \sqrt{2}
\]

### Step 2: Use the property \(\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}\)

\[
\sqrt{5} \times \sqrt{10} = \sqrt{5 \times 10} = \sqrt{50}
\]
\[
\sqrt{5} \times \sqrt{2} = \sqrt{5 \times 2} = \sqrt{10}
\]

### Step 3: Combine the results

\[
\sqrt{50} + \sqrt{10}
\]

### Step 4: Simplify \(\sqrt{50}\)

\[
\sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}
\]

Thus, the final simplified form is:

\[
5\sqrt{2} + \sqrt{10}
\]

This is the simplest form of the given expression.

Would you like further clarification on any part of the process?

Here are 5 related questions for deeper understanding:
1. How can you simplify radical expressions involving multiplication?
2. What are the properties of square roots that are used for simplifying expressions?
3. Can \(\sqrt{50}\) always be simplified, or are there cases where it cannot?
4. How does distributing work when there are square roots involved?
5. How would you handle expressions with cube roots instead of square roots?

**Tip:** Always look for perfect square factors inside square roots to simplify them easily!

Simplify the expression: √5 (√10 + √2)

Learn how to simplify the radical expression √5(√10 + √2) step by step. This solution explains the distributive property with square roots, covers key algebraic concepts, and shows how to simplify expressions with radicals. Suitable for students in Grades 9-12.

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