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!