Hi, Frank here.

Golden Week is the perfect time to relax and dive into some math problems at your own pace。With a cup of coffee in hand, I’m tackling them slowly and steadily。

Today is Day 3 of my math journey。I’m using “High School Math Once Again” as a reference to review high school mathematics。

Since I’ve always been a bit math-challenged, I’m just following the core topics from the book and rewriting the explanations in my own words to make them easier to understand。

Reference Book: “High School Math Once Again” by Kazuo Takahashi, published by Nihon Jitsugyo Publishing Co., Ltd。

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・”To compare irrational numbers, square them to eliminate the square root” — that’s the basic strategy。

With that fundamental in mind, I jumped into Exercise 3, which mixes rational and irrational numbers。

At first, numbers like \(\sqrt{5}\) and \(\sqrt{\frac{9}{2}}\) threw me off a bit。But after squaring both the irrational and rational numbers to compare them, I managed to get both questions right！

Then I moved on to rationalizing denominators in monomials and polynomials。Paying close attention to the prime factor decomposition of the denominator, I used the “difference of squares” technique。I’m happy to say that I nailed both questions in Exercise 4 as well。

However, when it came to finding the integer and decimal parts of an irrational number, I made a small mistake。I used the correct inequality signs but wrote the larger numbers on the left, when the correct answer had them arranged from the right。Oops (chuckle)！

Polynomials with roots in the denominator were definitely the toughest challenge today。So I wrapped up my study session by memorizing some approximate values of irrational numbers:

\(\sqrt{2}\) = 1.41421356 “Hi-to-yo, Hi-to-yo, Ni Hi-to-mi-go-ro”
\(\sqrt{3}\) = 1.7320508 “Hi-to-na-mi-ni O-go-re-ya”
\(\sqrt{5}\) = 2.2360679 “Fu-ji-san-ro-ku Ō-mu-na-ku”
\(\sqrt{6}\) = 2.449489 “Ni-yo-yo-ku Yo-ya-ku”
\(\sqrt{7}\) = 2.6457513110 “Tsu-mu-ji-kon-nan Koi-san Ii-rei” (my own silly mnemonic 😄)

Just a little “approximated pun fun” to wrap up the day！

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