https://file.aiquickdraw.com/mathbot/file/1729737060774gigme2qo.jpg

The problem asks to multiply and simplify by factoring:

\[
\sqrt{15} \cdot \sqrt{21}
\]

First, use the property of square roots that allows us to multiply them:

\[
\sqrt{15} \cdot \sqrt{21} = \sqrt{15 \cdot 21} = \sqrt{315}
\]

Next, we simplify \(\sqrt{315}\). Start by factoring 315:

\[
315 = 3 \cdot 105 = 3 \cdot 3 \cdot 35 = 3^2 \cdot 5 \cdot 7
\]

Now, since \(3^2\) is a perfect square, we can take it out of the square root:

\[
\sqrt{315} = \sqrt{3^2 \cdot 35} = 3\sqrt{35}
\]

Thus, the simplified expression is:

\[
3\sqrt{35}
\]

Would you like more details or have any questions?

Here are some related questions:
1. How do you multiply square roots in general?
2. What is the importance of factoring in simplifying square roots?
3. Can you simplify \(\sqrt{35}\) any further?
4. How would the answer change if the square roots contained negative numbers?
5. What if the problem involved cube roots instead of square roots?

**Tip:** Always look for perfect squares within a number to simplify the square root more easily.

Multiply and simplify by factoring: √15 · √21

Learn how to multiply and simplify the square roots √15 and √21 using factoring techniques. This problem demonstrates key algebraic concepts, including the properties of square roots and factoring methods. Suitable for students in Grades 8-10.

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