【Mathematics】What Are Numbers?(2)Real Numbers~Rational and Irrational Numbers (Rules for Arithmetic Operations with Square Roots)~

Hi, it’s Frank.
説明文

I spent the morning doing laundry today. Since this week is an adjustment week for my online lessons, there are no teaching sessions scheduled. That means I can take my time and go about things slowly and calmly—including the laundry. With no rush or pressure, even chores feel relaxing.

To be honest, I don’t use a fully automatic machine—I do my laundry semi-automatically. Why? Because by manually filling the tub with water, I get a bit of arm exercise. I also do some stretches and grip training while I’m at it, which helps me maintain muscle strength.

It might sound like something from the Showa era, but surprisingly, it’s a great way to refresh myself and lift my mood.

So, here we are on Day 2. As usual, I’ll be continuing my high school math studies using Mō Ichido Kōkō Sūgaku as my reference.

Since I’ve never been great at math, I’m sticking only to the core topics for structure. I’ll be rewriting the content in my own simplified and original style, so I appreciate your understanding.

【Reference Book】『Mō Ichido Kōkō Sūgaku』by Kazuo Takahashi, published by Nihon Jitsugyō Publishing Co., Ltd.

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・A rational number is “a number that can be expressed as a fraction.”
・An irrational number is “a number that cannot be expressed as a ratio of integers.”

These two points are fundamental.

Since square roots (a square root of X) are included among irrational numbers, I focused today on learning how to perform the four arithmetic operations with square roots.

That means practicing how to add, subtract, multiply, and divide square roots. After reviewing a few examples involving prime factorization (factorization in prime numbers; factorization into prime factors; prime factor decomposition [PFD]), I jumped right into Exercise 2.

To my surprise (and delight?), I got all six problems correct. It’s been a while since I used a pencil so intensely—my fingers are definitely sore! When you spend most of your time typing on a keyboard, just using a pencil for a while can make your arms and fingers ache.

The book emphasized that in prime factorization, you should “let out what needs to come out,” so I guess constipation is a no-go. (Yep, math humor.)

To be honest, as of today, I still don’t feel like I fully understand “rational numbers” and “irrational numbers,” so I plan to take my time and gradually deepen my understanding.

Full comprehension? “Muri-ssu!” (← That’s a Kansai-style pun. “Muri” means “impossible,” and it also sounds like “irrational.”)

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Frank

■ Frank Yoshida is an award-winning author who made his professional debut in January 2009 after winning the Grand Prize in the “Gateway to Success for New Writers 2008” Contest, sponsored by Goodbook Shuppan, Japan. His acclaimed short love story, Hanarerarenaku-nacchau (“What Would I Do Without You?”), marked the beginning of his published literary journey. He holds a Bachelor of Arts in Economics from Kobe University of Commerce. ■ Frank brings a wealth of international business experience to the table. With a strong background in Surface Mount Technology (SMT), he served as a technical adviser in key innovation hubs such as Silicon Valley, Hsinchu (Taiwan), and San Jose (California). His global career includes negotiating international investment disputes in the United States, advising in the leather industry, and managing timber import strategies. As a seasoned international business consultant and flexpatriate, he has worked extensively across North America, Latin America, Oceania, Southeast Asia, Europe, and Africa for leading trading companies and multinational clients. ■ A certified English expert, Frank holds ten prestigious English qualifications: UNATE (United Nations Association Test of English) SA Class, BEST (Business English Standard Test) A-Grade, Volunteer Interpreter Test (V-Tsuken) A-Grade, TOPEC (Nursing English) Perfect Score, Nissho Business English Proficiency Test Grade 1, Tourism English Proficiency Test Grade 1, Zensho English Proficiency Test Grade 1, English Vocabulary Test (TANKEN) Grade 1, EIKEN® Grade 1, and Japan's National Government Licensed Guide Interpreter certification. ■ Frank is also a passionate motorcycle enthusiast. He finds his ultimate freedom cruising along scenic coastlines aboard his beloved Suzuki Hayabusa GSX-1300R mega tourer. He describes the liberating experience in two words: “Stay aloof.”

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