To find the square root of \(1,368,900\), let’s proceed step-by-step:

\[
\sqrt{1,368,900}
\]

1. **Prime factorization method (optional, insight):**
   - Start with \(1,368,900\) and factor it into primes:  
     \(1,368,900 = 100 \times 13,689\).  
     \(100 = 10^2\), so we only need to focus on \(\sqrt{13,689}\).

2. **Finding the square root directly:**
   - Use a calculator or estimation method:
     \[
     \sqrt{1,368,900} = 1170
     \]

Thus, the square root of \(1,368,900\) is:

\[
\boxed{1170}
\]

### Verification:
\[
1170^2 = 1170 \times 1170 = 1,368,900
\]
This confirms our answer is correct.

Would you like a breakdown of the estimation method? Or any other questions?

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**Here are five related questions you might find interesting:**
1. How do you estimate square roots without a calculator?
2. What are perfect squares, and how do they differ from numbers like \(1,368,900\)?
3. Can every positive number have both a positive and negative square root?
4. How does the prime factorization method help in finding square roots?
5. What is the concept of irrational square roots, and when do they occur?

**Tip:** Memorizing squares of numbers up to 30 (like \(30^2 = 900\)) helps with quick square root estimations.

Learn how to find the square root of 1,368,900 with a detailed step-by-step solution, including verification and insights into the prime factorization and square root properties. Perfect for students in Grades 6-8.

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