Question: tell me how to do surds

Amy Mason answered on 18 Nov 2024:

Surds are a huge topic in maths – whole PhDs are written about the mathematics created by using them, One of the topics in my undergraduate degree was on “Algebraic Number Theory”, which is about studying the sets you get when you add a single surd, like the square root of 2, to the set of rational numbers. The rational numbers are the ones you get from fractions of whole numbers e.g. 1/2 or 76/1145. It can be interesting to think about what other numbers you can get from these numbers just using addition, multiplication, subtraction and division. You can get to (1+ sqrt(2))/17 but you can never get to sqrt(3). Then you can think about what equations can be solved in different sets.

So I can’t tell you have to do surds, because there are so many things you can do with them. I recommend googling if you have a specific question, or finding a book that talks about surds. “Mathematics for the Million” is a good introduction to a lot of different maths topics.