Hi, there!
Have you ever let out a roar, “Eureka!”? The word stems from the Greek language, which means “I have found it!” The discovery should bring the greatest happiness when it is attributed not to the fruit of serendipity but to your arduous efforts.
When I was a second-grade junior high school student, I used to go to a library with my best friend after school when I didn’t have activities at the soft-ball tennis club. He taught me a lot about solving mathematics and always stayed by me until I could reach the correct answer to mathematical word problems.
One day I loosed a whoop of Eureka after solving an intricate problem, almost spending two hours racking my brain trying to figure it out.
――”You’ve made it!” said my friend, beaming right in my face.
It was the moment I determined I would definitely help him whenever he was in dire need.
Today I try to answer a word problem by rationalizing the denominator of a fraction. Do you know why? Because “rationalizing” means “Yuu-rika” in Japanese. Don’t let out a chuckle at my cheesy joke, OK?
Rationalize the denominator of \(\frac{8 + 2\sqrt{6}}{8 – \sqrt{24}}\).
Here is my solution to the problem.
\(\frac{8 + 2\sqrt{6}}{8 – \sqrt{24}}\)
\(= \frac{(8 + 2\sqrt{6})(8 + \sqrt{24})}{(8 – \sqrt{24})(8 + \sqrt{24})}\)
\(=\frac{64 + 16\sqrt{6} + 8\sqrt{24} + 2\sqrt{6・24}}{64 – 24}\)
\(= \frac{11 + 4\sqrt{6}}{5}\)
I’ve finally rationalized the fraction; however, I’m not 100 percent sure whether it conforms to the KISS principle.
Stay tuned, and expect to see my next post.
Keep well.
Frank Yoshida
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【グローバルビジネスで役立つ数学】でもっと学習する b＾＾)
【参考図書】『もう一度高校数学』（著者：高橋一雄氏）株式会社日本実業出版社
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