$$ \sqrt{\frac{169}{10000}}=\sqrt{\left(\frac{\placeholder{}}{\placeholder{}}\right)^2} $$$$ =\frac{\placeholder{}}{\placeholder{}} $$$$ = $$

Let's solve the given expression step by step.

We are given:

\[
\sqrt{\frac{169}{10000}} = \sqrt{\left(\frac{\placeholder{}}{\placeholder{}}\right)^2}
\]

### Step 1: Simplifying the square root

We know that the square root of a fraction can be written as the square root of the numerator divided by the square root of the denominator:

\[
\sqrt{\frac{169}{10000}} = \frac{\sqrt{169}}{\sqrt{10000}}
\]

### Step 2: Finding the square roots of the numerator and denominator

- $\sqrt{169} = 13$
- $\sqrt{10000} = 100$

So, we now have:

\[
\frac{\sqrt{169}}{\sqrt{10000}} = \frac{13}{100}
\]

Thus:

\[
\sqrt{\frac{169}{10000}} = \frac{13}{100}
\]

### Step 3: Filling the placeholders

The placeholders would be filled as:

\[
\sqrt{\left(\frac{13}{100}\right)^2} = \frac{13}{100}
\]

So the complete equation is:

\[
\sqrt{\frac{169}{10000}} = \frac{13}{100}
\]

Would you like further clarification or additional details on any step?

### Relative Questions:
1. How do you simplify square roots of fractions?
2. What is the property of square roots that allows splitting the fraction?
3. How would you solve $\sqrt{\frac{49}{144}}$?
4. Why is it important to recognize perfect squares in such problems?
5. Can you apply the same method to irrational numbers in the square root?

### Tip:
When solving square roots of fractions, remember that the square root of a fraction is the square root of the numerator divided by the square root of the denominator.

Solve: $$ \sqrt{\frac{169}{10000}} = \sqrt{\left(\frac{\placeholder{}}{\placeholder{}}\right)^2} $$$$ =\frac{\placeholder{}}{\placeholder{}} $$$$ = $$

Learn how to simplify the square root of a fraction, such as $$ \sqrt{\frac{169}{10000}} $$, step by step. This guide explains key concepts in square roots and fractions, including simplifying perfect squares, suitable for Grades 6-8 students.

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