Abstract—Presenting Figures in surd form is relatively common in science and engineering especially where a calculator is either not allowed or unapproachable, and the computations to be undertaken involve irrational values. Every pupil who plans to take computation’s at the advanced position in such a calculus-based or statistics should be suitable to manipulate and deal with surds. The purpose of Peter Chew’s Theorem is to make solving the Quadratic Surds problem simple by converting any value of the Quadratic Surds √(a + b√c) into the sum or difference of two real numbers. Peter Chew’s theorem also converts square roots of complex numbers into complex numbers because square roots of complex numbers are also Quadratic Surds √(a + b i) =√(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 tutoring and mathematics literacy. 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, this makes online calculators unable to solve Quadratic Surds problems. This can lead to reduced student interest and hinder the spread of technology tool use. In order to solve the above problems, my research is to create a new discovery for the Quadratic Surds problem, such as Peter Chew’s theorem, so that all problems can be easily solved 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.

Keywords—Peter Chew theorem, quadratic surds, surds, Peter Chew

Cite: Peter Chew, "Peter Chew Theorem and Application," International Journal of Applied Physics and Mathematics, vol. 14, no. 4, pp. 106-113, 2024.

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