To simplify the square root of 48 (√48), follow these steps:

1. **Find the prime factorization of 48**:
   \[
   48 = 2 \times 24 = 2 \times 2 \times 12 = 2 \times 2 \times 2 \times 6 = 2 \times 2 \times 2 \times 2 \times 3 = 2^4 \times 3
   \]

2. **Group the factors into pairs**:
   \[
   48 = (2^2 \times 2^2) \times 3
   \]

3. **Simplify the square root**:
   \[
   \sqrt{48} = \sqrt{(2^2 \times 2^2) \times 3} = 2 \times 2 \times \sqrt{3} = 4\sqrt{3}
   \]

So, the simplified form of \( \sqrt{48} \) is:
\[
4\sqrt{3}
\]

Would you like further explanation on this?

Here are some related questions:
1. How do you simplify higher-order radicals?
2. What are the rules for simplifying cube roots?
3. How does prime factorization help in simplifying radicals?
4. What is the difference between rational and irrational numbers?
5. How do you multiply and divide radicals?

**Tip:** When simplifying square roots, look for perfect squares in the factorization to pull out of the radical!

Learn how to simplify the square root of 48 (√48) by using prime factorization. Follow the step-by-step method to break down 48 into its prime factors, group the factors, and simplify the radical to 4√3. This guide is perfect for students in Grades 8-10 learning to simplify square roots.

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