**Conclusion**

Today you get square roots with many correct decimal places instantly with your calculator or computer. However, as we saw with the fourth and fifth approximations of \(\sqrt{5},\) far greater accuracy can be achieved by means of a few easy calculations invented more than 800 years ago.

**About the Author**

Friedrich Katscher was born in Vienna in 1923. He is a lifelong Viennese who studied theoretical physics and mathematics and was science editor of a newspaper. Since the 1960s, he has been active as a historian of mathematics, giving lectures at the Vienna Technological University (Technische Universität Wien) and specializing in Italian Renaissance mathematics. His ability to speak German, English, French, Italian, and Spanish aids him in his mathematics history research. He invites you to correspond with him about this article and about Italian Renaissance mathematics via email (dr.katscher.vienna@chello.at).