To simplify the square root of 162, we can factor it into its prime factors and look for any perfect square factors.

First, let's factor 162:

$162 = 2 \times 81$ $81 = 9 \times 9 = 3 \times 3 \times 3 \times 3$

So, the prime factorization of 162 is:

$162 = 2 \times 3 \times 3 \times 3 \times 3 = 2 \times 3^4$

Now, we can simplify $\sqrt{162}$:

$\sqrt{162} = \sqrt{2 \times 3^4}$

Recognizing that $3^4$ is a perfect square $(3^2)^2$, we can simplify further:

$\sqrt{162} = \sqrt{2 \times (3^2) \times (3^2)} = 3 \times 3 \times \sqrt{2} = 9\sqrt{2}$

So, the square root of 162 in simplest radical form is $9\sqrt{2}$.

Would you like to explore more examples or have any questions?

Here are 5 related questions for further practice:

1. Simplify $\sqrt{72}$ into simplest radical form.
2. What is the square root of 50 in simplest radical form?
3. Express $\sqrt{200}$ in simplest radical form.
4. Simplify $\sqrt{98}$ into simplest radical form.
5. How do you simplify the square root of a non-perfect square?

Tip: When simplifying square roots, always look for the largest perfect square factor to extract the simplest form.