Let's solve the given problem step by step:

The expression is:

$\frac{\sqrt{162}}{\sqrt{9}}$

Step 1: Simplify the square roots

We can simplify the square root in the denominator first:

$\sqrt{9} = 3$

So the expression becomes:

$\frac{\sqrt{162}}{3}$

Step 2: Simplify the square root of 162

Now, let's simplify $\sqrt{162}$. We begin by factoring 162:

$162 = 81 \times 2$

Since $81 = 9^2$, we can take the square root of 81:

$\sqrt{162} = \sqrt{81 \times 2} = 9\sqrt{2}$

Step 3: Substitute and simplify the expression

Substituting $\sqrt{162} = 9\sqrt{2}$ into the expression, we get:

$\frac{9\sqrt{2}}{3}$

Now, simplify the fraction:

$\frac{9\sqrt{2}}{3} = 3\sqrt{2}$

Final Answer:

The expression in its simplest radical form is:

$3\sqrt{2}$

Would you like any additional details or have any questions?

Here are 5 follow-up questions to expand on the topic:

1. How would you simplify an expression like $\frac{\sqrt{98}}{\sqrt{4}}$?
2. Can you simplify $\sqrt{50}$ in radical form?
3. What is the general rule for simplifying fractions with square roots?
4. How can you express $\sqrt{a \times b}$ in terms of individual square roots?
5. What would happen if the denominator of the fraction had a non-perfect square?

Tip: Always try to factor square roots by identifying perfect squares, as this makes simplification much easier.