Peter Chew Theorem and Application

Abstract. Presenting numbers in surd^ form is quite common in science and engineering especially where a calculator is either not allowed or unavailable, and the calculations to be undertaken involve irrational values 1 . Every student planning to study math’s at the senior level in such a calculus-based or statistics course should be able to manipulate and deal with surds2. The purpose Peter Chew Theorem 3 is to make it simple to solve the problem of quadratic roots, by converting any value of the Quadratic Surds √[(a+b√(c)] into the sum or difference of two real numbers. Peter Chew Theorem can also convert the square root of a complex number into a complex number , because the square root of the complex number is also the quadratic surd √(a+bi) =√[a+b√(-1)]. In addition, Peter Chew's Theorem can also convert Quadratic Surds √[a+b√(c)] into the sum or difference of two complex number [√z +√(z ̅)]. Technical tools have had a significant impact on advanced mathematics teaching and mathematics learning. However, today's online calculator only contains the knowledge that has been explained in the book, but the current method cannot or is difficult to solve some Quadratic Surds problems, which makes the online calculator unable to solve the Quadratic Surds problems. This will cause students to reduce interest and hinder the promotion of the use of technical tools. In order to solve the mention problems, my research is to create a new discovery (Peter Chew theorem) for the topic of Quadratic Surds, so that all problems can be easily solved, and then apply Peter Chew’s theorem to a AI Age calculator (Peter Chew Quadratic Surd Diagram calculator), allow the AI Age calculator to solve any problem in the topic of Quadratic Surds, which can make the AI Age calculator effectively help mathematics teaching, especially in the future when similar COVID-19 problems arise. The purpose of Peter Chew's Theorem for Quadratic Surds is the same as Albert Einstein's famous quote Everything should be made as simple as possible, but not simpler