The value of \( \sqrt{150} \) can be simplified as follows:

First, break down 150 into its prime factors:
\[
150 = 2 \times 3 \times 5^2
\]

Now, apply the square root:
\[
\sqrt{150} = \sqrt{2 \times 3 \times 5^2}
\]

Since \( \sqrt{5^2} = 5 \), we can simplify:
\[
\sqrt{150} = 5 \times \sqrt{6}
\]

Thus, \( \sqrt{150} \) simplifies to:
\[
\boxed{5\sqrt{6}}
\]

Would you like further details on the process or have any other questions?

Here are 5 related questions to explore:
1. What is \( \sqrt{200} \) simplified?
2. How can we estimate \( \sqrt{6} \) to a decimal value?
3. How do we calculate cube roots like \( \sqrt[3]{150} \)?
4. What are the properties of square roots of prime numbers?
5. How can \( \sqrt{150} \) be used in solving quadratic equations?

**Tip:** When simplifying square roots, always check for perfect squares in the factorization!

Discover how to simplify the square root of 150 using prime factorization. Learn the step-by-step process to break down 150 into its prime factors and simplify \( \sqrt{150} \) into 5\( \sqrt{6} \). Suitable for students in Grades 8-10.

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