https://file.aiquickdraw.com/mathbot/file/1726073205383q1o831bu.jpg

The image shows the expression \(\sqrt{\frac{5}{2}}\), which is the square root of the fraction \( \frac{5}{2} \).

To simplify this:

\[
\sqrt{\frac{5}{2}} = \frac{\sqrt{5}}{\sqrt{2}}
\]

We can rationalize the denominator by multiplying the numerator and denominator by \( \sqrt{2} \):

\[
\frac{\sqrt{5}}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{5} \times \sqrt{2}}{2} = \frac{\sqrt{10}}{2}
\]

Thus, the simplified form of \( \sqrt{\frac{5}{2}} \) is:

\[
\frac{\sqrt{10}}{2}
\]

Would you like further details on this process or have any specific questions?

Here are 5 related questions you might find helpful:
1. How do you simplify the square root of a fraction?
2. Why is rationalizing the denominator important?
3. How do you approximate square roots like \( \sqrt{10} \)?
4. Can square roots of fractions always be simplified this way?
5. What are other methods for simplifying square root expressions?

**Tip:** When working with square roots of fractions, always check if the denominator can be simplified or rationalized for easier handling.

Learn how to simplify the square root of the fraction 5/2. This problem involves rationalizing the denominator and applying square root properties to algebraic expressions. Suitable for Grades 9-10 students learning square roots and rationalization techniques.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation