https://r2.erweima.ai/mathbot/image/172604463119169ruxiva.jpg

The expression in the image can be interpreted as follows:

\[
3 \cdot \sqrt{\frac{1}{4} + \frac{1}{9}}
\]

Let's break it down step-by-step:

1. **Add the fractions inside the square root:**
   To add \(\frac{1}{4}\) and \(\frac{1}{9}\), we need a common denominator. The least common denominator (LCD) of 4 and 9 is 36.

\[
\frac{1}{4} = \frac{9}{36}, \quad \frac{1}{9} = \frac{4}{36}
\]

Now add them:

\[
\frac{9}{36} + \frac{4}{36} = \frac{13}{36}
\]

2. **Square root of the result:**

\[
\sqrt{\frac{13}{36}} = \frac{\sqrt{13}}{6}
\]

3. **Multiply by 3:**

\[
3 \cdot \frac{\sqrt{13}}{6} = \frac{3\sqrt{13}}{6} = \frac{\sqrt{13}}{2}
\]

So, the final answer is:

\[
\boxed{\frac{\sqrt{13}}{2}}
\]

Would you like further details or clarification on any step?

Here are 5 related questions for practice:
1. How would the result change if we replaced \( \frac{1}{4} \) with \( \frac{1}{16} \)?
2. What is the decimal approximation of \( \frac{\sqrt{13}}{2} \)?
3. How can you simplify \( \frac{1}{9} + \frac{1}{16} \) using the same process?
4. What happens if you remove the square root and solve \( 3 \times \left( \frac{1}{4} + \frac{1}{9} \right) \)?
5. How do you calculate the square root of a fraction in general?

**Tip:** To add fractions, always find the least common denominator (LCD) to make the addition easier.

Learn how to solve 3 * sqrt(1/4 + 1/9) by adding fractions and simplifying the square root. This detailed solution involves the properties of square roots and addition of fractions, perfect for students in Grades 8-10.

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