Today is 5/5/25, making it Square Root Day because 5 x 5 = 25. The last Square Root Day was 4/4/16 and our next one will be 6/6/36. Here are some fun square root facts that you can share today: 

• A whole number with a square root that is also a whole number is called a perfect square. The days on which we celebrate Square Root Day are all examples of perfect squares, since we don’t have decimal days or months. 

• Negative numbers do not have square roots, since multiplying a number by itself will always give a positive (i.e. -4 x –4 = 16). However, you can express the square root of a negative number by using imaginary numbers (4i x 4i = -16). 

• We don’t know where exactly the square root symbol came from. Some theories say Arab mathematicians used the first letter in the Arabic word for root, while others believe it came from the Latin letter “r,” which is also the first letter in the Latin word for root.  

• The radix we use today was created by Descartes, who combined two previously used notation symbols.  
• The ancient Mesopotamians might have calculated a square root approximation by using a sequence of rectangles(1). There’s a Mesopotamian tablet from the Old Babylonian period that contains square root calculations expressed exclusively with vertical wedges representing ones and tens arranged relationally to each other.(2)  

Special thanks to collaborator Carol Hollier from the Sciences Library for her contributions to this blog post.

References:

1. Daniel F. Mansfield (2023) Mesopotamian square root approximation by a sequence of rectangles, British Journal for the History of Mathematics, 38:3, 175-188, DOI: 10.1080/26375451.2023.2215652 
2. C. Proust, Interpretation of reverse algorithms in several Mesopotamian texts, in The history of mathematical proof in ancient traditions, 384–422, translated by Micah Ross, Cambridge Univ. Press.  See chart on page 21 of the preprint: https://hal.science/hal-01139635/file/12Proust-pp.pdf