手算平方根或立方根

本研究旨在解決目前的高中數學教材中，已經不再教授開平方的直式開方法，更遑論求三次方根，學生無需使用計算機就能算出平方根或三次方根，僅僅在課綱中要求學生會估計平方根的近似值即可。然而在統計部分的單元學習過程中，仍有些題目會要求學生計算某些牽涉到平方根統計量的近似值，例如標準差。在筆者的教學經驗中，也常有學生會問如何開平方根，因此筆者將在此篇文章中，先以尺規作圖找出有理數的近似值以及無理數的近似值，接著能用十分逼近法求根式的近似值最後以國小時的九九乘法表為基礎，導入平方與平方根的意義使用標準分解式以求出完全平方數的平方根，最終介紹所謂的直式開方法來解決平方根與三次方根近似值的問題。

關鍵字

立方根

並列摘要

The purpose of this study is to deal with the unit that is not taught in the current high school mathematics textbooks longhand method , let alone the cube root. Nowadays, students can extract the square root or cube root without using a computer, they are only required to estimate the approximate value about the square root in math course outline. However, in the learning progress of some certain statistics unit, there are topics asking students to solve the square root approximate value, such as standard deviation. In my teaching experience, there are some students asking me how to extract the square root. Therefore, I will find the approximate value about rational number and irrational number first with compass-and-straightedge construction; then, I will find the approximate value by using euclidian algorithm. Next, I will use multiplication Practicing” to introduce the meaning of square and square root and get the “square root of a perfect square” by using standard decomposition. Finally, I will introduce the longhand method and express how to cope with the approximate value of square or cube root.