The expression \(\sqrt{12} \times \sqrt{27}\) can be simplified using the property of square roots that states:

\[
\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}
\]

So, let's first multiply the numbers under the square roots:

\[
\sqrt{12} \times \sqrt{27} = \sqrt{12 \times 27}
\]

Now, calculate \(12 \times 27\):

\[
12 \times 27 = 324
\]

Thus:

\[
\sqrt{12} \times \sqrt{27} = \sqrt{324}
\]

The square root of 324 is:

\[
\sqrt{324} = 18
\]

So, the simplified result is:

\[
\sqrt{12} \times \sqrt{27} = 18
\]

Would you like more details on this or have any questions?

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1. How do you simplify square roots with different bases?
2. What are the rules for multiplying radicals?
3. Can you always combine square roots by multiplication?
4. How do you find the square root of non-perfect squares?
5. How does the property \(\sqrt{a} \times \sqrt{b} = \sqrt{ab}\) work for negative numbers?

**Tip:** When multiplying square roots, always check if the result can be simplified further by taking the square root of the product.

Learn how to simplify \(\sqrt{12} \times \sqrt{27}\) with detailed step-by-step instructions. This problem involves multiplying square roots and applying the multiplication of radicals formula. Suitable for Grades 7-9.

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