Okay, I need to create a professional and useful wiki document about square roots in Korean, following the given structure and requirements. me start by understanding the's query.

The category is Education, sub Math, and more specifically High School Math. The title is "제곱근 which is Square Root in. The document should be in markdown format with a hierarchy of headings (H1, H2, H3), an introduction, detailed sections, and possibly references. It needs to be at least 800 characters long, which in Korean would be around 200-300 words, but I should aim for more to be thorough.

First, the title as H1. Then an overview section explaining what square roots are. I should make sure to define them clearly, maybe mention that they are the inverse of squaring. Then, under the overview, perhaps a brief history or origin of the concept.

Next, the detailed sections. The user mentioned using H2 and H3. Possible H2 sections could be "제곱근의 정의", "제곱근의 성질", "제곱근 계산 방법", "응용 분야", and "관련 개념". Each H2 can have H3 subsections if needed.

For the definition, I need to explain that the square root of a number x is a number y such that y² = x. Also note that positive numbers have two square roots, positive and negative, but the principal root is the non-negative one. Mention the radical symbol √. Maybe use examples like √4 = 2, but also clarify that √9 is 3, not ±3. Also, touch on irrational numbers here, like √2 being irrational.

In the properties section, list key properties: product of square roots, quotient, power rules. For example, √(a*b) = √a * √b, and √(a/b) = √a / √b. Also, √(a²) = |a|. These should be explained with examples to make them clear.

Calculation methods: Maybe include manual methods like the Babylonian method or long division. But since this is high school level, perhaps focus on simplifying radicals and using calculators. Also, mention how to rationalize denominators, like multiplying numerator and denominator by √2 to rationalize 1/√2.

Applications: Where are square roots used? Geometry (Pythagorean theorem), quadratic equations, standard deviation in statistics, physics equations. Provide specific examples, like finding the hypotenuse of a right triangle.

Related concepts: Square roots vs. cube roots, irrational vs. rational numbers, quadratic equations. Maybe explain how square roots relate to solving x² = a.

Need to ensure that technical terms are explained. For example, if I mention "근사값" (approximate value), I should clarify it. Also, use markdown elements like bullet points, tables if needed, and code blocks for any calculations, though maybe not necessary here.

Check for accuracy: Make sure that the principal square root is non-negative, correct properties, correct examples. Avoid common misconceptions, like √x² = x (which is incorrect, it's |x|).

Structure-wise, after the introduction, each H2 section should flow logically. Use headings and subheadings appropriately. Maybe include a "참고 자료" section at the end with links to textbooks or online resources.

Now, start drafting each section. Make sure the language is clear and suitable for high school students. Use simple explanations with examples. Check the length to ensure it's over 800 characters. Let me count the characters as I go, but in Korean, each character is a Hangul, so 800 characters would be sufficient. However, aiming for around 1000-1500 characters would be better to meet the requirement comfortably.

Wait, the user said the document should be in Korean, so I need to write everything in Korean. Let me confirm the terminology. For example, "Babylonian method" might be translated as "바빌로니아 방법" or kept as is. Also, "Pythagorean theorem" is "피타고라스 정리" in Korean.

I should also make sure that mathematical symbols are correctly represented. In markdown, using LaTeX for math is possible, but if the user wants standard markdown without LaTeX, maybe use Unicode symbols. For example, √ for square root, ² for squared.

Potential issues to avoid: Confusing square roots with solutions to equations. For example, x²=4 has solutions ±2, but √4 is 2. Emphasize this distinction.

Also, include examples of irrational numbers and why they are important. Maybe mention that √2 is irrational and how that was discovered historically.

For the history part, perhaps mention ancient Babylonians or Greeks. Theaetetus in ancient Greece worked on irrational numbers.

In applications, quadratic equations can be solved using square roots after completing the square. Also, in statistics, standard deviation uses square roots of variance.

Check if all sections are covered and that the content is comprehensive but not too advanced for high school level. Avoid complex topics like complex numbers or higher-order roots unless necessary.

Finally, proofread for clarity and correctness. Ensure that each section flows into the next and that the document meets all the user's requirements.