the square root of 32 and the square  root of 2 and the square root of 8 = < >

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!

the square root of 32 and the square root of 2 and the square root of 8 = < >

Learn how to simplify and compare square roots, including √32, √2, and √8. Discover step-by-step solutions using properties of square roots and algebraic comparison. Suitable for students in Grades 6-8.

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