Let's break down the expression:

\[
5\sqrt{2} \times \sqrt{18}
\]

### Step 1: Simplify \(\sqrt{18}\)
The number 18 can be factored as \(18 = 9 \times 2\), and we know that \(\sqrt{9} = 3\). So:

\[
\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}
\]

### Step 2: Multiply the terms
Now substitute \(\sqrt{18}\) with \(3\sqrt{2}\):

\[
5\sqrt{2} \times 3\sqrt{2} = 15 (\sqrt{2} \times \sqrt{2})
\]

We know that \(\sqrt{2} \times \sqrt{2} = 2\), so:

\[
15 \times 2 = 30
\]

### Final Answer:
\[
5\sqrt{2} \times \sqrt{18} = 30
\]

Would you like further details or have any questions?

Here are 5 related questions to consider:
1. What is the result of \(4\sqrt{3} \times \sqrt{12}\)?
2. How do you simplify square roots with larger numbers?
3. Can you explain the process of rationalizing a denominator with square roots?
4. What happens when you multiply two different

Learn how to multiply radicals with this step-by-step guide on solving 5√2 × √18. This problem demonstrates simplification of square roots and the product of radicals, suitable for students in Grades 6-8.

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