To evaluate and compare the expressions involving the square roots of 32, 2, and 8, let's break them down individually:

1. $\sqrt{32}$:
   We can simplify $\sqrt{32}$ as: $\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2}$ So, $\sqrt{32} = 4\sqrt{2}$.

2. $\sqrt{2}$:
   This is already in its simplest form. So, $\sqrt{2}$ remains $\sqrt{2}$.

3. $\sqrt{8}$:
   We can simplify $\sqrt{8}$ as: $\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}$ So, $\sqrt{8} = 2\sqrt{2}$.

Now, let's compare them:

• $\sqrt{32} = 4\sqrt{2}$
• $\sqrt{8} = 2\sqrt{2}$
• $\sqrt{2} = \sqrt{2}$

Clearly, we can see the following relationship: $4\sqrt{2} > 2\sqrt{2} > \sqrt{2}$ So, $\sqrt{32} > \sqrt{8} > \sqrt{2}$.

Would you like more details or have any questions?

Here are 5 related questions:

1. What is the square root of 50 simplified?
2. How do you compare two square roots that aren't easily simplified?
3. Can you use a calculator to compare the values of $\sqrt{32}$ and $\sqrt{8}$?
4. How do square roots relate to exponent rules?
5. What happens when you square a square root?

Tip: When simplifying square roots, always look for perfect squares within the number, as they make the expression easier to handle!