To simplify the square root of \( \frac{15}{4} \), we follow these steps:

\[
\sqrt{\frac{15}{4}} = \frac{\sqrt{15}}{\sqrt{4}}
\]

Since \( \sqrt{4} = 2 \), we get:

\[
\frac{\sqrt{15}}{2}
\]

The square root of 15 cannot be simplified further because 15 is not a perfect square. Therefore, the simplified form is:

\[
\frac{\sqrt{15}}{2}
\]

Would you like more details or have any questions about this?

Here are some related questions to explore:

1. How would you simplify \( \sqrt{\frac{25}{9}} \)?
2. What is the approximate decimal value of \( \frac{\sqrt{15}}{2} \)?
3. Can you express \( \sqrt{15} \) in terms of prime factorization?
4. What happens if you multiply \( \sqrt{\frac{15}{4}} \) by 2?
5. How do you simplify the square root of \( \frac{9}{16} \)?

**Tip:** When simplifying square roots of fractions, simplify the numerator and denominator separately.

Learn how to simplify the square root of 15/4 with a detailed step-by-step solution. Understand the process of simplifying square roots of fractions by separating the numerator and denominator. Suitable for students in Grades 8-10.

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