I was browsing the wiki page for “Square root of 2” where I saw a picture of a clay tablet dated about 1700 BCE. Apparently it is a Babylonian approximation for the square root of 2. But really it is a square with some markings. How do researchers know that what they are looking at is significant?
Image is found here: https://commons.m.wikimedia.org/wiki/File:Ybc7289-bw.jpg#mw-jump-to-license
Because every archeological evidence is significant. Every single shard of pottery tells a story of trade, exploration, technical achievements and wealth. When you find text like this it is very important as it is then possible to read what the ancient people were thinking and not have to interpret them from their artifacts. What you are looking at is a form of text known as Cuneiform. This is an ancient form of text used in the Bronze age and would later transform into Greek and then on to Latin which is what the Western and Central European language use as a writing system. Any archeologist would recognize Cuneiform and a lot of people are actually able to read and write it fluently today, although the language it is written in is another matter. We do actually have a lot of Cuneiform tablets as they used to write on clay that they would fire. This would make the text last for thousands of years. Later writings used papyrus or other cheaper biodegradable materials and we have a lot less texts from those. The clay tablet you mention is just one of 40.000 Cuneiform tablets in the collection which is only the 6th largest collection of Cuneiform tablets in the world. There is a lot of text to go through so there is likely a lot more treasures like this. However it is likely that people were attracted to this tablet because in addition to the text there is diagrams which explains what the numbers mean. This is unusual for Cuneiform tables and it also makes it obvious to any casual observer that the tablet likely contains some scientific explanation as this is where you have the need for symmetrical constructed diagrams.