Let's solve the expression: 

\[
\sqrt{\frac{81}{100}} - \sqrt{\frac{4}{25}}
\]

### Step 1: Simplify each square root term individually.

1. \(\sqrt{\frac{81}{100}} = \frac{\sqrt{81}}{\sqrt{100}} = \frac{9}{10}\)
2. \(\sqrt{\frac{4}{25}} = \frac{\sqrt{4}}{\sqrt{25}} = \frac{2}{5}\)

### Step 2: Perform the subtraction.

We need to subtract \(\frac{2}{5}\) from \(\frac{9}{10}\). To do this, we must first have a common denominator:

\[
\frac{2}{5} = \frac{4}{10}
\]

Now, subtract the fractions:

\[
\frac{9}{10} - \frac{4}{10} = \frac{5}{10} = \frac{1}{2}
\]

### Final Answer:
\[
\sqrt{\frac{81}{100}} - \sqrt{\frac{4}{25}} = \frac{1}{2}
\]

Would you like any further details or clarifications?

Here are 5 related questions you might find interesting:
1. What is \(\sqrt{\frac{64}{49}} - \sqrt{\frac{25}{36}}\)?
2. How do you simplify expressions with multiple square roots in fractions?
3. Can you explain how to rationalize denominators involving square roots?
4. How would you solve \(\sqrt{\frac{121}{144}} + \sqrt{\frac{16}{49}}\)?
5. What is the geometric meaning of square roots in terms of area?

**Tip:** When subtracting fractions, always find a common denominator before subtracting!

Learn how to simplify the expression √81/100 - √4/25 with a detailed step-by-step solution. This math problem covers key concepts such as square roots of fractions and basic arithmetic operations. Suitable for students in Grades 6-8.

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