https://file.aiquickdraw.com/mathbot/file/1726831869150ehkw7hjd.jpg

The expression to simplify is:

\[
\frac{\sqrt{3} \times \sqrt{6}}{\sqrt{72}}
\]

### Step-by-Step Simplification:

1. **Multiply the square roots in the numerator:**
   \[
   \sqrt{3} \times \sqrt{6} = \sqrt{3 \times 6} = \sqrt{18}
   \]
   
2. **Simplify the square root of 18:**
   \[
   \sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}
   \]

3. **Simplify the square root of 72 in the denominator:**
   \[
   \sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} = 6\sqrt{2}
   \]

4. **Now divide the expressions:**
   \[
   \frac{3\sqrt{2}}{6\sqrt{2}} = \frac{3}{6} = \frac{1}{2}
   \]

### Final Answer:
\[
\boxed{\frac{1}{2}}
\]

Would you like further details or explanations?

### Related Questions:
1. How do you multiply two square roots?
2. What are the properties of square roots that help in simplification?
3. How do you simplify a square root that involves a perfect square?
4. What is the process of rationalizing the denominator in square root expressions?
5. How do you handle fractional exponents?

### Tip:
When simplifying square roots, always look for perfect squares within the number to make simplification easier!

Simplify the expression: (sqrt(3) * sqrt(6)) / sqrt(72)

Learn how to simplify the square root expression (sqrt(3) * sqrt(6)) / sqrt(72) with detailed steps. This example covers key algebraic concepts like the product of square roots and simplification of radicals, suitable for Grades 7-10.

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