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Presenting numbers in surdform 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. 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 surds. The purpose Peter Chew Theorem is to let upcoming generation solve same problem of Quadratic Surds can solve simple and directly compare what`s now solution. Therefore, applying Peter Chew's theorem to Algebra problems(Finding Roots of a Quadratic Equation with Real Coefficients) can help to solve some Algebra (Quadratic Equation) problems more easily . 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. The 2nd Edition adds more information about important of Surd and updates some information.