https://file.aiquickdraw.com/mathbot/file/1727438545330dcywykz1.jpg

In the image, we have two expressions involving square roots:

**(a)** \( \sqrt{9} \cdot \sqrt{90} = 3 \cdot 3\sqrt{10} = 9\sqrt{10} \).

This simplifies the multiplication of square roots by:
1. \( \sqrt{9} = 3 \), since the square root of 9 is 3.
2. \( \sqrt{90} \) can be simplified to \( \sqrt{9 \times 10} = \sqrt{9} \times \sqrt{10} = 3\sqrt{10} \).
3. Finally, multiply \( 3 \times 3\sqrt{10} = 9\sqrt{10} \).

So the final result is \( 9\sqrt{10} \).

**(b)** \( \sqrt{3} \cdot \sqrt{6} = \sqrt{18} \).

This can be simplified:
1. Multiplying the square roots \( \sqrt{3} \times \sqrt{6} = \sqrt{3 \times 6} = \sqrt{18} \).
2. \( \sqrt{18} \) can be simplified as \( \sqrt{9 \times 2} = 3\sqrt{2} \).

Thus, \( \sqrt{3} \cdot \sqrt{6} = 3\sqrt{2} \), and the expression provided in the image, \( 3\sqrt{9} \), is incorrect. The simplified answer is actually \( 3\sqrt{2} \).

Would you like any further clarification or details?

Here are 5 related questions to expand your understanding:
1. What are the properties of square roots when multiplying two square roots together?
2. How do you simplify square roots like \( \sqrt{90} \) or \( \sqrt{18} \)?
3. Can square roots of negative numbers be simplified in the same way?
4. What is the relationship between perfect squares and simplifying square roots?
5. How does the distributive property work with square roots in expressions like these?

**Tip**: Remember, when multiplying square roots, you can combine the numbers inside the roots and simplify after.

Solve the following square root expressions: a) √9 · √90 = ?, b) √3 · √6 = ?

Learn how to simplify square root expressions like √9 · √90 and √3 · √6 with detailed step-by-step solutions. This guide covers essential algebraic concepts such as multiplication of radicals and simplifying square roots. Suitable for students in Grades 8-10.

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