To simplify \( \sqrt{40} \), follow these steps:

1. Factor 40 into its prime factors: 
   \[
   40 = 2^3 \times 5
   \]
   
2. Group the factors to simplify the square root. We can rewrite \( \sqrt{40} \) as:
   \[
   \sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10}
   \]

3. Simplify \( \sqrt{4} \), which is 2:
   \[
   \sqrt{40} = 2\sqrt{10}
   \]

So, the simplified form of \( \sqrt{40} \) is:
\[
\boxed{2\sqrt{10}}
\]

Would you like to explore more on this topic or need further clarification?

Here are 5 questions to deepen your understanding:
1. How do you simplify other square roots like \( \sqrt{72} \)?
2. What is the square root of 50 in its simplest form?
3. How can you express \( \sqrt{a^2 \times b} \) in simplified form?
4. How does simplifying square roots relate to factoring numbers?
5. What is the difference between simplifying square roots and calculating their decimal approximations?

**Tip:** When simplifying square roots, always look for perfect square factors to make the process easier.

Learn how to simplify the square root of 40 using prime factorization and the product property of square roots. This solution simplifies \( \sqrt{40} \) to \( 2\sqrt{10} \). Suitable for students in Grades 6-8.

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