![[Why] 제곱근의 성질이 성립하는 이유는? 루트 안이 자연수일때? 분수, 실수일 때?](https://i1.gguge.com/r/teacher/b86d0895-4155-4497-bc4d-ad38e618b67f.png.webp?w=1280)
[Why] 제곱근의 성질이 성립하는 이유는? 루트 안이 자연수일때? 분수, 실수일 때?
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'자연수 범위'에서 성립하는 제곱근의 성질은, 수 범위를 유리수까지지 확장하여도 성립합니다. 그러나 많은 학생들은 왜 그렇게 되는지 이유를 알지 못하고 외우기만 하여 제곱근 계산에 어려움을 겪습니다. 복잡하지 않고 간단한 증명으로 그것을 배울 수 있는 수업입니다.
Class Type
One Day
Ages
14-16
Class Size
Max 5people
Duration
30min
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구자익
Reviews
191
🧠 왜 루트 성질이 (수 범위에 상관없이) 항상 맞을까? 증명으로 확실하게 배우는 시간
제곱근을 풀 때 “이거 그냥 외우면 되지!”라는 생각 해본 적 있나요?
하지만 분수나 실수, 복잡한 수로 들어가면 왜 그렇게 되는지 헷갈릴 수 있어요.
이 수업에서는 단순한 암기가 아니라, 수의 범위를 확장해도 제곱근의 성질이 왜 항상 유지되는지 직접 증명해보며 이해력을 키울 거예요. 공식의 이유를 알게 되면, 계산 실수도 훨씬 줄어드니까 수학 시간이 훨씬 쉬워질 거예요.
✨ 수업 후 아이는 이렇게 성장해요
제곱근 규칙이 자연수, 분수, 실수에서 어떻게 성립하는지 명확하게 설명할 수 있어요
수학 공식을 그냥 외우지 않고, ‘진짜 이유’를 이해하는 경험을 해요
자기 손으로 간단한 증명을 완성하며 논리력과 자신감을 키워요
새로운 유형의 제곱근 문제도 당황하지 않고 접근해요
📝 수업 내용 3줄 요약
자연수부터 분수, 실수까지 단계별로 제곱근의 성질을 살펴봐요
증명 활동을 통해 왜 그런지 스스로 확인해요
복잡한 제곱근의 곱셈과 나눗셈일 때도 제곱근 계산에 자신감이 생겨요
🌈 이런 아이에게 추천해요
제곱근 공식이 왜 맞는지 궁금한 중학생
수학 문제 풀이에서 증명 파트가 막막한 학생
외우는 것보다 이해하고 싶은 수학 학습자
실수~유리수 범위에서 제곱근 계산에 자신이 없는 친구
🔎 수업은 이렇게 진행돼요
5분: 오늘의 주제와 공식 소개, 궁금증 나누기
10분: 자연수에서 제곱근 성질 증명 따라하기
10분: 분수/실수로 범위 확장, 직접 증명해보기
5분: 이해 체크 퀴즈 & 질의응답
💡 왜 공식이 성립하는지 확실하게!
아이들이 “이건 그냥 외우면 돼”라고 말할 때, 진짜 원인을 알면 수학에 즐거움을 느끼고 실수도 적어져요. 자기 손으로 증명해보고, 수학적 호기심을 키울 수 있도록 도와줄게요. 쉽고 간단한 접근법으로, 복잡한 수학 공식도 확실히 내 것으로 만들어보세요!

Great for These Kids
제곱근의 성질 이해에 어려움을 겪는 학생
제곱근의 곱셈과 나눗셈 문제를 자주 틀리는 학생
제곱근의 성질이 수 범위 확장에도 성립하는 이유가 궁금한 학생
중등수학 3-1 1단원 제곱근과 실수 단원을 배우지 않은 학생
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If the teacher cancels the class, you will receive a full refund and any coupons used will be restored.
Teacher Info
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구자익
Reviews
191
Graduated from Korea University (Seoul Campus) Served as the Director of a renowned academy in the Gangnam 3-gu district for over 15 years Personally produced over a dozen textbooks for elementary, middle, and high school students Taught a student who achieved a perfect score on the 2016 CSAT starting from their first year of high school. For 15 years, I taught middle school classes for medical school and top-tier students, as well as high school classes for Grade 1 students and Grade 1 CSAT students in the Gangnam 3-gu district of Seoul. As an academy director for 10 years, I gained diverse experience teaching students of various levels. In particular, the teacher has the strength of reading students' thoughts, quickly identifying their habits, and presenting appropriate countermeasures and methods. Through the teacher's diverse teaching experience and student observations, countless students have gained confidence in mathematics and improved their grades. Mathematics is a discipline that organizes complex thoughts and aids in problem-solving. In other words, it is a subject that is truly essential to us. However, nowadays, students view mathematics as a subject where they must memorize concepts and theories (without critical analysis) and repeatedly solve problems by type (without knowing why they are solved that way). Mathematics is based on operations, and as students advance through the grades, they must learn by connecting and expanding upon new concepts and theories with what they have already learned. However, students who strongly believe that mathematics is solely about operations face limitations because they view the subject through this single lens. Consequently, the better a student's calculation skills are, the more difficult middle school mathematics feels. This difficulty is experienced again when learning high school mathematics. Mathematical concepts and theories require students to develop a habit of proactively understanding them, while problem-solving requires problem analysis and solution strategies. Only by learning "the connection and expansion of mathematical concepts" and "problem analysis, understanding, and problem-solving strategies" will students realize that mathematics is simple and easy as time goes by. The teacher will help students come to this realization. The teacher's teaching method is somewhat unique. 1. The teacher explains "why" concepts and theories are necessary, "how" they are expressed in a particular way, and "what" they connect to among previously learned concepts. 2. The teacher provides students with the opportunity to express their own thoughts. This allows the teacher to distinguish between well-thought-out ideas and those that need correction. 3. Understand the student's thought process regarding 'how' they solved the problem. 4. Teach how to analyze and understand problems, and the starting point for solving them. 5. Do not teach by categorizing problems into types. Therefore, do not teach solution methods by categorizing them either. 6. Regularly check whether the student solved the problem correctly (logically), and encourage them to express their thoughts verbally (verbal expression helps them identify their weaknesses).
Experience & Activities
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Teaching middle and high school subjects to middle and high school students for approximately 20 years
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Coaching for various competitions such as KJMO, KMO, and AMC
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Producing numerous successful applicants to electronics high schools and specialized high schools
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Producing numerous students with Grade 1 high school GPA and CSAT scores in the Gangnam 3 districts for over a decade
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Produced perfect scorers on the CSAT (2016 academic year)
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Selling books personally created by the teacher at Kyobo Book Centre (search for JIK)
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International school IB classes or AP courses (Pre-Algebra, Algebra, Geometry, Combination, Number Theory, Pre-Calculus, Calculus)
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